There having BEEN no buses, we had to walk home.

The simple answer is, "There being no buses, we had to walk home." I also agree with GDS' answer which uses "having been". This is a participle clause - it actually doesn't have a tense (don't mistake it for present continuous) and just describes the situation at the moment of the main action. Notice that we don't need any connecting-words. :) "There were no buses, so we had to walk home." is perfectly correct in all varieties of English, but it misses the point of the grammar exercise you're doing.

The first answer is the American way to say it. The second is the British way to say it.

There were no buses, so we had to walk home.