Well, when I was growing up in Tulsa I never took the bus; you know you're in trouble when your bus is labeled "clockwise" or "counterclockwise"
When I moved back here three years ago from Chicago, I tried out the buses quite a few times over the course of about 6 mos. The buses are usually either ontime, or within 10-15 mins of ontime. When it was cold/snow/ice, I was surprised to find how easy it was to simply call TulsaTransit (582-2100) and be told how much of a delay there was....
http://tulsatransit.org/The bad news is the daytime bus routes don't run much past 7 or 7:30pm. Saturday service is limited and there is no Sunday service. "Nightline" service (after 8pm) consists of a handful of vans that run so rarely (every hour or two) that you should budget for cabbing it home unless you're lucky enough to find one. The fares recently increased to $1.50 cash fare a few months ago, but you can get a 10-ride pass for $12 or a monthly pass for $40. There are also day and week passes but I recommend the 10-ride passes because of the new policy on free transfers.
The good news is that when you board the bus, you should always ask for a free transfer, even though I guess this is now called a "U2" pass. "U2" will give you "unrestricted access" for 2 hours (3 hours on Saturdays). Which is great because you can use it for your return trip if you are just going somewhere for lunch or doing an hour's worth of shopping, etc... the buses are really bike friendly with two bike racks in front, and if you don't have a bike, the downtown station offers the adventurous a free bike and lock for the day...
You can buy bus passes at any QuikTrip store; there's one right across the street from the football stadium on 11th Street. I'd also buy a Tulsa Transit "traveler"-- a full schedule with maps that only costs fifty cents... don't know if they're available at QT... if not, you should get one at the downtown bus station. I liked carrying it with me at all times, because the bus routes stop making sense the closer they get to downtown...
Your daytime buses in the TU area are:
#210 Harvard (North/South but you can take the north bus to the downtown station)
#111 11th Street (East/West)
#215 15th Street (East/West)
#221 21st Street (East/West)
Your nightline options are:
#860 (board on 11th St) and #880 (board on 21st St)
TulsaTransit has only two "hubs" -- 4th & Denver (downtown across from the new arena but also down the street from the courthouse and the county jail, safe during the day, be careful later at night) and the one you will likely never go to at S. 34th St and Memorial Dr.
Hope this helps.