I never thought I’d be advocating for the 2A, but...
If, by "British Bill of rights" you mean https://avalon.law.yale.edu/17th_century/england.asp then it seems to be clearly concerned that a standing army in peace time is a concern, and places a limit on it (specifically, that it require consent of Parliament). It doesn't strike me as remotely contradictory to think that those drafting the 2nd Amendment might have thought that did not go quite far enough, and have chosen a slightly different tack in addressing the same concern.
This certainly leaves room for other evidence to decide the question in either direction, but (assuming I correctly interpreted your reference) the thing that you presented as evidence for your position doesn't seem to be.