I can't comment about Bisley because I don't shoot there.
The BFTA card is a national registration card for members of affiliated clubs. Under the terms of the insurance scheme that has been negotiated on behalf of the BFTA members, you are only covered if you have a shooter's card. If you join a BFTA affiliated club, you will automatically receive a shooter's card.
Information about gradings, as well as quite a lot of other stuff, is available on the BFTA official website at http://www.airgunshed.co.uk/bfta