Actually, they are both fine. As far as the topic（私は） is at the beginning and the verb(帰ります) at the end, word order is not so important when you construct sentences in Japanese. If I really have to choose either one, I;l The connection(relationship) between 家へ and 帰ります looks a bit stronger than バスでand帰ります. Therefore I don't feel like to break the stronger connection

Hi there! Technically, both sentences are correct. The difference between 1 and 2 is If you want to make sure which transportation you will use, then you should say, 私はバスで家へ帰ります。 （地下鉄や電車、タクシーではなく、私はバスを利用して家へ帰る、という感じで受け止められます。） If you want to describe where you want to go, you should say, 私は家へバスで帰ります。 （友達の家や親せきの家ではなく、自分の家へ帰るということが強調されています） But to think about the situations, I suppose 2 won't usually happen. Because, you always go back to your house, right? So you don't need to emphasize [家へ]　at all That's why 1 is more natural than 2.

This is a representation of me. 私は　バスで家へ　帰る。or 私は　バスで家に　帰る。 試験問題には通用しない答えかも・・・sorry.

either is ok! however, i like the former. i think, in actual conversation, we say just ''バスで帰ります''.