Probably a good question for "ask the staffer"! There are different types of factors from what I know:

1) the "permanent" (e.g. many airports charge different amounts for bus/walk/bridge gates so some airlines pick walk or bus gates on purpose to reduce costs);

2) the "structural" (for instance there may always be a bus element in some airports if a plane arrives as domestic but leave as international or vice versa; airports will try to maximise the use of bridges in terms of movements and passengers, so they will often prefer to allocate bridges to the largest planes that can be accommodated in a given gate, and to flights which means that the gate use can be maximised as opposed to being left empty for 2 hours in between rotations; some times are busier than others and increase the risk of bus gates; similarly, in some busy airports, airports try to "share" the burden of bus gates equitable - for instance I know that at NCE in the summer season, they make a point to discuss with airlines early on and "share" bridge space so that BA, LH, etc each get 1-2 bus gates a day but the rest is bridge);

3) the "there and then" (as mentioned by others, gates available at given points in time especially if a plane is early or late, etc

Some airports accommodating long haul planes with long time on the ground tend to disembark at a gate and then ask them to leave the gate only to return later (I've seen it at some Australian airports for instance), but most will just leave the plane at the gate to disembark and embark again so typically it's either bridge or bus for both disembarkation and embarkation unless one is domestic and one international (happens quite a bit for LHR T5 when BA planes which arrive from abroad into a domestic gate where they are positioning for the next flight, so even though passengers are technically connected, they still need to be bussed to international arrivals, same for AF at CDG when a plane arrives from non-Schengen notionally at 2E (e.g UK, some of Eastern Europe) to then fly to Schengen notionally from 2F or the other ways round.