Hello, Christopher. I'm not sure how much experience you have in creating network datasets, so please feel free to ask if you need any clarification on any of the following. Multimodal networks tend to be pretty complicated.
But before I continue, I'll just mention that there is a set of tools you can download to take care of a lot of this automatically if you have GTFS public transit data: http://www.arcgis.com/home/item.html?id=0fa52a75d9ba4abcad6b88bb6285fae1
To answer your question, if you want the bus stops to be incorporated as part of your network, you need to do a couple of things:
1) You need to make sure the geometries are connected. You can use the Snap geoprocessing tool to snap the transit stops to the street features. But if you need to maintain the transit stops in their original locations (for instance, because they are connecting the transit lines), then it would be best to create a copy of the stops first and snap the copy. You can then use the Points to Line geoprocessing tool to generate a connector line between the original stop location and the new stop location. The Points to Line tool can make use of the stop's ID to generate an individual line between each pair of stops with the same ID (the original and the snapped version).
2) In order for your stops and connector lines to actually be connected in the network dataset, you need to add vertices to the street features at the locations of connection. You can do this automatically by running the Integrate tool with 0 xy tolerance. Make a back-up copy of your data first because Integrate can do some scary and non-reversible things.
3) In addition to the above, you need to include the stops, snapped stops, and connector lines into your network dataset as network data sources. Use a connectivity policy of Override for your snapped stops if you have End Point connectivity for your streets. This ensures that the connector lines connect to the streets at the vertices you created and don't have to snap to end points.
