Learn Russian: Автобус едет вперёд.

In English, a bus simply 'goes', but Russian has specific verbs for going on foot versus going by transport. We use едет (from the verb ехать) because a bus is a vehicle. Note: You might also hear Russians say a bus идёт when talking about its scheduled route, but едет specifically emphasizes the physical action of driving.

Could we use ездит instead of едет here?

Not for this exact meaning. Both verbs mean 'to go by transport', but едет is a unidirectional verb of motion. We use it here because the bus is making a single, one-way movement right now (forward). Ездит is a multidirectional verb used for repeated actions, like a bus driving its daily route back and forth.

Why does the word вперёд end in the letter д but sound like a 'т' when spoken?

This happens because of a common Russian pronunciation rule called 'devoicing'. When a voiced consonant like д is at the very end of a word, it is pronounced like its unvoiced partner, which is т. So, you will hear native speakers say 'вперёт'.

How would I say the bus is moving backward?

You would replace вперёд with its exact opposite, which is the adverb назад (backward or back). The sentence would become Автобус едет назад.