The match will take place on Saturday, August 22, although the club have not confirmed a kick-off time.
Bedford will be the second Championship side Albion will play in pre-season. Graham Dawe’s new-look team will open their warm-up campaign with a match against Jersey at St Peter on August 8.
Dawe said: “Playing Bedford at home is a really great fixture to have, but it will not be an easy encounter. It will certainly test the make-up of our team.
“We have now confirmed fixtures against Jersey and Bedford and we are also looking for another game.”
Bedford and Albion were the two longest serving teams in the Championship until Plymouth’s relegation in April.