For info on the Bartons Arms discussion, here is the bus gen; The buses are National Express West Midlands 33/51 to Walsall/Pheasey from Lower Bull Street/High Street stop BS16 (down the road from the Peaky Blinder bar to see on a map). They jointly run every 5 mins, journey time about 7 mins to Burlington Street, 2 mins from the pub.
Note that the starting point might be subject to change due to ongoing tram extension works (needs checking nearer the time).

The current fare appears to be £2.40 single, £4 day ticket, £7 group day ticket for up to 5 people. Twerly passes valid after 09.30. Mobile app tickets available and cash & contactless accepted on the bus.