Many aspects of discrete choice are made more difficult when there are correlations between the choices / attributes of the options (often results in probit rather than more elementary logit formulation). Thus, for example the presence of more buses may lower traffic count, but the stop / start pattern of transit could make the free flow travel time only an approximate measure of the link performance.

I recommend "Route Choice: Wayfinding in Transport Networks" by P.H.L. Bovy and E Stern published by Kluwer in 1990. The section called "elements" around p 100 is very good on the issue you raise. I'd say that the bottom line would that congestion (no matter what form it takes) is going to provoke modification of routes, and that the resulting equilibrium traffic assignment follows fundamental traffic engineering principles (user equilibrium). Whether you can get some additional quality into the behavioral predictions by altering the mix of vehicle types is probably going to take some further digging.

I guess what you are looking for can be found in traffic assignment literature.

However, if you consider the demand to be inelastic (fixed) and the volumes of buses are known, the problem is a simple single class traffic assignment problem and can be solved by any traffic assignment algorithm, according to the wardrapian principle (beckman optimization model)

In a more general case, the demand can be calculated by a

maybe you can use GIS software by network processing  the program choose the best  route in relations to presence of public transport vehcles