Monday nights at Freedom Bar in Anonas, Q.C.. Akasha will handle the main set then jammers are welcome to join after. Another relatively new and building scene is at Tago Bar in Main Ave. Q.C. every friday night. Paolo Blaquera trio plays there and jammers can join in and after the set. Those are the places I'm familiar with.
For both places, it's on the jammers to bring their own instrument. I thinks it's not the exact setup that you have in mind with a piano, upright bass on the stage but it's quite close. They play standards . The jam session in Tago can go to anything goes depending on the people who are playing.