On main match days some trains stop at Bordesley. Not sure if they do for friendlies though. If not then Small Heath would be the nearest on that line. Its about 1 mile from the ground.
Can you get there from New Street?
New Street doesn't serve Bordesley but Moor Street does, the chances of a train stopping there though are slim. You're better off getting a taxi, bus or just walk it, takes about half an hour to walk and is a straight forward route.