Surprisingly, perhaps not.
The Pottermore article about the Hogwarts Express (transcript) ends with this passage:
Many pure-blood families were outraged at the idea of their children using Muggle transport, which they claimed was unsafe, insanitary and demeaning; however, as the Ministry decreed that students either rode the train or did not attend school, the objections were swiftly silenced.
The same article explains the problems the Ministry and the school faced when a large number of students travelled by magical means, including:
- The risk of accidents when carrying trunks or pets (brooms)
- Unspecified problems when trying to apparate into the Hogwarts grounds
- “Portkey-sickness” among young children
Even if the Ministry decree was lifted in later years, these problems would persist. I’m inclined to think that they didn’t, given that proud pure-bloods like Malfoy still ride on the train.
However, worth noting that @rsegal’s suggestion of the Knight Bus is entirely plausible given the above. From the Pottermore article about King’s Cross Station (transcript), we get approximate dates for when the Hogwarts Express entered service:
It was Evangeline Orpington, Minister from 1849–55, who hit upon the solution of adding a concealed platform at the newly (Muggle) built King's Cross station, which would be accessible only to witches and wizards.
Sometime in the early 1800s. (It’s not clear where the train departed from before they constructed the concealed platform at King’s Cross.)
Also from Pottermore, we learn when the Knight Bus (transcript) was first used:
Finally, Minister for Magic Dugald McPhail hit upon the idea of imitating the Muggles’ relatively new ‘bus service’ and in 1865, the Knight Bus hit the streets.
So there had been at least ten years of Hogwarts Express-only transport to Hogwarts before the Knight Bus came into play. The Ministry may have relaxed the decree for the Knight Bus, although I don’t think many people would have used it – far too uncomfortable, if nothing else.