It's hard to give a definitive answer to this question, but here are what I think are the two most likely possibilities:
The most direct route from the third-floor corridor to the owlery passes through the entrance hall.
It is possible that there are areas of the castle that are divided, such that one would have to go up/down in order to get to the connecting point. That is to say that the third-floor corridor may be separated from the Owlery in such a way that the only way to circumvent the barrier is to go down to the entrance hall, move laterally along the castle in an area where there is no barrier, and then go back up to the owlery from the other side of the barrier.
I believe this can be supported from an earlier passage in Philosopher's Stone. When Harry and friends set off from Gryffindor Tower to the trophy room to meet Malfoy for the midnight duel, part of their journey is described as follows:
They sped up a staircase to the third floor and tiptoed toward the trophy room.
Note the word "up". As they were coming from Gryffindor Tower they should have been going down to get to the third floor, not up. The fact that they needed to go up would support the theory that there are some areas that are separated from each other in a way that requires one to go down out of the way and then back up. Since the third-floor corridor is also on the third floor, it is entirely reasonable that this would apply to it as well. Indeed, at the end of the book when they are actually going from Gryffindor Tower to the third-floor corridor, the same phrase is used:
They didn't meet anyone else until they reached the staircase up to the third floor.
We can possibly support this further by going back to Dumbledore's announcement about the third-floor corridor at the beginning of the term:
"And finally, I must tell you that this year, the third-floor corridor on the right-hand side is out of bounds to everyone who does not wish to die a very painful death."
It is not entirely clear to me what "the right-hand side" is referring to. It might mean that there is one big third-floor corridor but only one end of it is out of bounds. That is to say that if you were to enter into the middle of the corridor you would be allowed to go to the left but not to the right. However, from the description of the corridor when they try to get past Fluffy, this appears to perhaps not be the case:
A few seconds later, they were there, outside the third-floor corridor — and the door was already ajar.
This sentence makes it sound like the entirety of the third-floor corridor was behind the locked door.1 If that is the case, then what did Dumbledore mean by specifying that the right-hand side is forbidden?
In line with the above theory, we could suggest that the right-hand side is referring to the right side of the castle itself. There may be two separate third-floor corridors — one on the right side of the castle and one on the left side of the castle — and it is only the one on the right side of the castle that is forbidden. Now we know from the quote in the question that the owlery is at the top of West Tower. If we assume that Dumbledore was speaking from a standard orientation, then the right side of the castle would be the east side of the castle. Thus, the owlery and the forbidden third-floor corridor are on opposite sides of the castle, and there may be a barrier that prevented one from simply moving laterally across the third floor from the east/right side to the west/left side, such that in order to get from the forbidden third-floor corridor to the owlery one would have to first descend to the entrance hall where there is no lateral barrier between the east/right side of the castle and the west/left side of the castle.
There was some obstacle that prevented Hermione and Ron from taking the most direct route to the owlery.
While there is no specific evidence that something prevented them at this particular time, we do know that on other occasions the direct route to the owlery was avoided, for instance, in Order of the Phoenix:
"Yeah, 'bye," said Harry and instead of turning right, he turned left, taking a longer but safer route up to the Owlery.
1. On the other hand, the description back at the midnight duel may seem to indicate otherwise:
Ducking under Peeves, they ran for their lives, right to the end of the corridor where they slammed into a door — and it was locked.
Here it appears that they were already in a corridor on the third floor and the door leading to the forbidden area was at the end of the corridor, in which case Dumbledore's terminology may have simply been referring to the part of the corridor beyond the door, which was the right side. However, we can potentially argue against this by noting Peeves's statement immediately prior to this:
"STUDENTS OUT OF BED!" Peeves bellowed, "STUDENTS OUT OF BED DOWN IN THE CHARMS CORRIDOR!"
Thus, it seems that the corridor they were in was the Charms corridor, rather than part of a generic third-floor corridor. Perhaps the Charms corridor simply leads to the third-floor corridor, and some corridors have names while others are simply called by their floor number.