yes very much possible that is the bussiest routes

Best way is to catch a train from Mughal Serai to Gaya.The train journey is about 3hrs (but yes there can be delays)...and there are a lot of trains between these two station. Mughal Serai is few kms outside Varanasi

It's around 240km and takes 3h30 by road and between 4 and 5 hours by train. If you went by taxi and left early I guess it would be possible as a day trip. If you wish to take the train it will take you to Gaya, which is 13km from Bodhgaya. It would be difficult to make it as a day trip by train, especially as Indian trains often run late.