Do not draw new ways.

For each bus route create a relation (second button down on the right in Potlatch, a completely separate panel in JOSM) and tag the relation as route=bus. The number of the bus can be entered in as ref=## or name=##, with, I think, ref more or less essential.

Then for each way (road) which is on the bus route make that way a member of the new relation. You may need to split the way (little scissors icon in Potlatch or ‘x’, on tools menu in JOSM) when the bus route diverges from it. If the route goes in both directions no more needs to be done, but if it only travels along the way in one direction then add either forward or backward depending on whether the direction of travel is with the orientation of the way or against it.

Bus stops are best added as separate nodes alongside the road, and can then be added to the appropriate relations.

Timetable information I know little about, but there are various tagging schemas for time based information.

I would thoroughly recommend looking at some examples. The ÖPNV-Karte http://www.öpnvkarte.de/ is an OSM-based map designed to show public transport information, and is a good way to find some complete examples.

Once relations have been built it is a good idea to check that they work with various tools (see the wiki).

HTH,

SK53