Vegas' bus system is well-integrated into Google Maps. Google Maps shows stops and routes and times and schedules for all RTC routes.
Right now, Google Maps is still showing the data that'll be in effect until September 17. You can see a map showing Boulder Station and the nearby stops here.
However, come September 18, the route that travels Boulder Highway, Route 107, is going away, to be replaced by the Boulder Highway Express (BHX). You can read all about the new service here. It looks like the closest stop from downtown will be across Boulder Highway at Las Palomas. Heading downtown, you can hop on near the light at Lamb/Desert Inn.
The new service will likely show up in Google Maps before you go.
I've taken the bus to and from Boulder Station at all hours without any concerns. Be sure to come back here and tell us how it worked for you.