There is no Weaver base for the BPS. Browning has a proprietary base that is poorly designed and it's made specifically for use with weaver type scope rings. Unfortunately that limits you to using a regular scope or a red dot that has a longer tube and needs two mounting locations. The cross-slots in the base are a U channel so if you want to use a Burris fast fire you will have to take a file to one of the slots to make it a bit wider and squared off so that the fast fire will fit. In addition they use a proprietary size screw as well that is difficult to match with standard scope base screw sizes.
Years ago I tried to get EGW to make me a custom picattiny rail for the Browning. After going back and forth with EGW for several months they must have finally given up and blew me off and I never heard back from them.
William at Sumtoy is a regular on this site. I have never used him for any work but he most certainly seems to be very attentive to the needs of folks on this forum. I would suggest reaching out to him to see if he can either make a base for the browning or re-drill and tap it so that it could take a standard Weaver or pic base. Good luck..
