行く→The bas don't go to the hospital yet 行った→The bas already went to the hospital

First, based on the sentence structure, options 2) and 3) are not possible, since it requires a noun-modifier for "bus (バス)", and thus either the plain-form (dictionary form) or "-ta (-た)" form (past tense of the dictionary form) can be used. In my personal point of view, If one is on the street, and there is a bus which goes to the hospital, then it should be "あれは 病院 へ行くバスです", i.e., option 1. If one is given a photo (or a video clip), and there shows a bus which goes to the hospital, then it would probably be "あれは 病院 へ行ったバスです", i.e., option 4. === 良い一日をお過ごしください。／I wish you a good day.

i would say あのバスは病院行きです

The sentence「あれは病院へ行ったバスです。」sounds strange to me...I think the correct answer is 「あれは病院へ行くバスです」. Sorry for lacking of explanation in detail, but using 行った in this case is unusual.