Yeah, I can see you were building in some slack for Birmingham drinking. The 144 gets you into Bromsgrove town centre nearly an hour quicker than your direct route, though, and its a stiff walk from the station.
TBH, I dont know pubs in Bromsgrove, but there are a number in the town centre, including between the bus station and the ground. The ground bar is also decent ... cant think the game will be segregated.
After the game, you should make the 17.10 from the bus station, but there is the 144 direct to New Street station going at the same time - and every 20 minutes if you want to be more leisurely.
Just checked and this weekend is not one that is scheduled for FA Cup Rounds (if either of us progress) - so is unlikely to be rearranged (I know, I know, ... reaching the 1st Round may seem fanciful ...)