^^^ Possibly, Barry, but that involves a change at Birmingham Moor Street.
Depending upon exactly whereabouts Baz will be starting from in the city centre, it might be simpler just to catch the direct train from Moor Street at 1037 or to pick up that same train one stop earlier, at 1033, from Snow Hill.
The fare's the same in each case anyway. (£4.20 single or £5 day return, reduced to £2.75 or £3.30 respectively for Senior Railcard holders).
PS: As I read it (but I strongly urge you to check for yourself), you can buy a ticket that gives you unlimited travel for a day on both buses and trains in the relevant area for £7.20:
https://legacy.wmnetwork.co.uk/tickets/#/ticket/39