If you're taking the free Mears shuttle, it picks up at the UO Transportation Center, which is between City Walk & the parking garages. Walk thru City Walk and take the moving sidewalks to the parking garages. At the end of the 2nd moving sidewalk (IIRC), there's a large round area where you choose which garage to continue on to. To the right of the moving sidewalk which goes to the garage on the right, there's an elevator down to the Transportation Center. There's also an escalator. At the bottom of the escalator or elevator, continue straight ahead to the bus stalls on the right. They usually use a large bus with an advertising wrap for BG, but on rare occasions there might be a generic Mears bus with a sign in the windshield.
You're complimentary shuttle includes return transportation. There is only one departure from BG, and you will usually be on the same bus. You're driver will tell you the time of the return, and remind you to remember your bus number.