I would probably draw in QuantumGIS and export as shapefile. There are many many ways to draw or otherwise generate spatial data. I think it depends on what you mean by 'effectively'?

Edit: Ok, I just re-thought your comment, and perhaps you mean to 'highlight' the existing road paths if they are also bus-routes. That would be trivial if your roads lines have attribute "bus_route". You can also add the attribute, then in QGIS you can select such paths, edit them and set the attribute as 'true', in TileMill you would then add a style to change color for lines with such attribute. Also, if the streets have names and you have a list of such streets, you can do a CartoCSS selection based on the street names attribute.

This is trivial - assign a value to an attribute for all segments that are part of a bus route, then style accordingly (preferably in a gis, the approach in the op is a cumbersome roundabout way)

Tilemill ingests geographic/spatial data, it doesn't have much provision for interacting with it.

You might find that someone has already drawn the bus routes you are interested in:

http://wiki.openstreetmap.org/wiki/Buses

(Then you just have the task of pulling the data out of OSM and translating it into a format that you can work with)

Also, I just realized, if the bus routes are not in the OSM, he could use the new iD editor and add the bus routes to OSM under his account, and then export :)