I don't know about your ID, but taking the greyhound from Montreal to Ottawa should be fine. The stations aren't always in great neighbourhoods, true, but stations in large cities are well-lit and have good security. Most times they are in the same building as the train station, and they will have a food court and other things available.
The buses themselves are OK. They are comfortable and quiet and most people are very nice. I've never had a problem. I do recall someone telling a driver she was bothered by a drunk, and he told her to tell him right away next time (she was telling him at the end of the trip after the drunk had left) as they can kick the person off the bus or call the police if there is a serious issue.
Some very small stations that are fine during the day close at night, leaving you stuck standing in dark alleys.
If you are stopping at a small town by yourself late at night and don't know what the station is like, get the number of the local cab service and have a car meet you there. Doesn't sound like that is going to be a problem on this trip, though.