No plausible canon explanation
The question asks us to compare the time it took Frodo to travel by pony from Rivendell to the Shire to the time it took Bilbo and the dwarves to travel by pony from the Shire to Rivendell (not the time it took Frodo to get from the Shire to Rivendell - that journey was largely on foot and not by road).
I don't completely agree with the travel times given in the question, so I will first explain my estimates and then compare them.
In order to avoid making a long post even longer, I have left out some quotes that might have been included. In particular, see Appendix D of The Lord of the Rings for details of when midsummer occurs and the number of days in each month.
In The Hobbit, Bilbo starts out with the dwarves at Bywater (a few minutes walk from Bag End), so we should compare that journey to Frodo's journey in The Lord of the Rings from Rivendell to Bywater.
Frodo: Rivendell to Bywater in 27 days
This is easy to calculate as Tolkien documents the journey in The Tale of Years
October 5. Gandalf and the Hobbits leave Rivendell.
6. They cross the Ford of Bruinen; Frodo feels the first return of pain.
28. They reach Bree at nightfall.
30. They leave Bree. The ‘Travellers’ come to the Brandywine Bridge at dark.
November 1. They are arrested at Frogmorton.
2. They come to Bywater and rouse the Shire-folk.
The Lord of the Rings Appendix B, Section 2: The Third Age
Page 1096 (Houghton Mifflin Harcourt; Single Volume 50th Anniversary Edition)
October 5 to November 2 is 27 days (October has 30 days in the calendar Tolkien is using). This is just one day longer than the 26 days stated in the question.
Bilbo: Bywater to Rivendell in 33 - 50 days
This one is harder to pin down and the best I can do is a range.
Departure from Bywater: April 28
The unexpected party at Bag End was in April
The dark came into the room from the little window that opened in the side of The Hill; the firelight flickered - it was April - and still they played on, while the shadow of Gandalf's beard wagged against the wall.
The Hobbit Chapter 1: An Unexpected Party
Page 13 (Unwin Books 1966 paperback edition)
It was late April. During the party, Gandalf tells Thorin
And Thrain your father went away on the twenty-first of April, a hundred years ago last Thursday
The Hobbit Chapter 1: An Unexpected Party
Page 24 (Unwin Books 1966 paperback edition)
If the party had been on a Friday, Gandalf would have said "a hundred years ago yesterday"; if it had been on a Thursday, he would probably have said "a hundred years and one week ago". So the party must be on Saturday through Wednesday, putting the date at April 23 through 27. The departure from Bywater was the next morning, between April 24 and April 28.
After a few days travel, it is May and what sounds like the Weather Hills come into sight (Bree is not mentioned by name, but it is presumably part of the "respectable country" with "an inn or two").
At first they had passed through hobbit-lands, a wild respectable country inhabited by decent folk, with good roads, an inn or two, and now and then a dwarf or a farmer ambling by on business. Then they came to lands where people spoke strangely, and sang songs Bilbo had never heard before. Now they had gone on far into the Lone-lands, where there were no people left, no inns, and the roads grew steadily worse. Not far ahead were dreary hills, rising higher and higher, dark with trees. On some of them were old castles with an evil look, as if they had been built by wicked people. Everything seemed gloomy, for the weather that day had taken a nasty turn. Mostly it had been as good as May can be, even in merry tales, but now it was cold and wet. In the Lone-lands they had to camp when they could, but at least it had been dry. "To think it will soon be June," grumbled Bilbo as he splashed along behind the others in a very muddy track. It was after tea-time; it was pouring with rain, and had been all day
The Hobbit Chapter 2: Roast Mutton
Page 29 (Unwin Books 1966 paperback edition)
Looking at Tolkien's maps, it seems that the Weather Hills should come into sight on the first day's ride from Bree. Merry tells us that Bree is a day's ride from Buckland and Appendix B tells us that it takes two days to ride from Buckland to Bywater.
The only way I can reconcile it being May in the passage quoted above with a departure from Bywater between April 24 - 28 is if they left Bywater on April 28, reached Buckland late on April 29, spent the night in Bree on April 30, and spotted the Weather Hills at tea-time on May 1.
Arrival at Rivendell: June 1 - 18
It is already June when they arrive at Rivendell. After they are met by elves outside Rivendell, we are told that:
Tired as he was, Bilbo would have liked to stay awhile. Elvish singing is not a thing to miss, in June under the stars, not if you care for such things.
The Hobbit Chapter 3: A Short Rest
Page 46 (Unwin Books 1966 paperback edition)
They stayed for "at least" 14 days in Rivendell.
They stayed long in that good house, fourteen days at least, and they found it hard to leave.
The Hobbit Chapter 3: A Short Rest
Page 47 (Unwin Books 1966 paperback edition)
They leave Rivendell on midsummer's day, which in Tolkien's calendar is two days after June 30.
The next morning was a midsummer's morning as fair and fresh as could be dreamed: blue sky and never a cloud, and the sun dancing on the water. Now they rode away amid songs of farewell and good speed
The Hobbit Chapter 3: A Short Rest
Page 50 (Unwin Books 1966 paperback edition)
As they left on midsummer's day and spent at least 14 days in Rivedell, they must have arrived no later than June 18. We know that it was June when they arrived, so the arrival must have been between June 1 and June 18 (probably towards the end of that period as it is hard to stretch "at least 14 days" to 31 days).
With a departure on April 28 and arrival between June 1 and June 18, the journey from Bywater to Rivendell must have taken 33 to 50 days (probably closer to 50 as noted above).
Why did it take Frodo less time than Bilbo
As stated in the question, Frodo's party were taking it easy on their way back to the Shire. This is illustrated by the fact that they didn't cross the Ford of Bruinen until the day after they left Rivendell (which is not far away) and that they spent a day in Bree (see the quote from Appendix B above).
On the other hand, the dwarves are on a mission and would not even let Bilbo return to Bag End for a pocket-handkerchief, a delay of less than 30 minutes.
"I'm awfully sorry," said Bilbo, "but I have come without my hat, and I have left my pocket-handkerchief behind, and I haven't got any money. I didn't get your note until after 10.45 to be precise."
"Don't be precise," said Dwalin, "and don't worry! You will have to manage without pocket-handkerchiefs, and a good many other things, before you get to the journey's end. As for a hat, I have got a spare hood and cloak in my luggage."
The Hobbit Chapter 2: Roast Mutton
Page 28 (Unwin Books 1966 paperback edition)
It is true that the dwarves are delayed almost a day by the trolls, but that is more than made up for by the extra day that Frodo spent in Bree.
Also, Bilbo and the dwarves had more hours of daylight (in May) than Frodo and his friends (in October) which would have allowed them to travel more miles per day. My conclusion is that there is no plausible canon explanation for the difference in travel times. Out of universe, I must conclude that this is a mistake by Tolkien.