All I can suggest is ask them at the interview stage, and be prepared for them to say 'no thanks'
Most bus companies expect new drivers to start on 'spare' work - i.e. you report at X time and then cover for anyone who reports sick, then you might go covering for holidays and longer term sick leave, then once a vacancy on a rota arises, you get a chance to go on to a regular rota. Some rotas will be more popular than others and may have a waiting list - for this sort of thing, seniority (i.e. length of service) usually gets first choice.
How long it takes to get on to a regular rota depends how big the depot is and what the staff shortage / turnover is like.
Some bus companies (and in the case of larger companies, some depots within those companies) do have a variety of rotas (in London for example, each rota tends mostly to work one or perhaps two routes), and some will have regular early turn / late turn / night shift / spreadover* rotas, or some that offer a regular (say) 45 hour rather than 40 hour week for those who want it. Likewise, an increasing number of operators do now have a proportion of part time drivers.
And depends where you work how much early morning / late evening / weekend work there is. In rural / 'small town' places, there's not that many buses that run outside the 0700 to 1900 Monday to Saturday range.
But generally it would be fairly unusual for a new driver to go straight on to this sort of thing (they might be more flexible for someone with an existing PCV licence)
Depends on the attitude of the operator / how eager they are to get new staff, I suppose.
* - in case this term doesn't make sense, a spreadover or split shift tends to mean working both peak hours with a long break between the two.
Some drivers like them (they tend just to be Monday to Friday, and some operator put them on a separate rota so you work them regularly and may or may not have any rostered weekend work) - but if you live any distance from depot, they can be a bit of a pain.
ETA - there's also usually a culture where it's acceptable to try and swap shifts with colleagues - different drivers prefer particular types of shift, so if you tended to want very early starts or lates, you might be popular. Having said that, all swaps need to be approved by a supervisor (mainly to ensure nobody ends up with a combination of shifts that breaches drivers hours law) and if you can't find anyone to swap with, that's your problem not the company's.
