Just ask a friendly Reading fan who lives in Bournemouth, not a bad start!
Its a long way I'm afraid, about 100 miles in total. Go M27, M3, and then off at Basingstoke and up the A33.
Or, you could try Hook A287, then through Hartley Wintney and across Hampshire through Eversley etc. Hampshire and its inbred land though is difficult to drive across what with poor roads. Alternatively come off the M3 at Winchester and go up the A34 then off at Chieveley Services and down the M4 towards London.
I'd go through Basingstoke and leave a bit of time. Best way on a matchday.