"I am an AC member, and I am GLD. Should I would like to shower there, is there a shower at BA's facilities I can use? Does the AC have showers?"

I think that you may be unable to go to the AC anyway since it is in the wrong terminal and unless travelling in Club Europe/Club World/First on with BA then you won't have access to the BA lounges as a OW Ruby member. If you do have lounge entitlement, then the BA Terraces does have showers.

Dave