From the Collins dictionary and others, Definition of Bowman is "an archer", doesn't state man or woman. I shoot at a club that uses Archers, so doesn't really count.
When you look how the word is used, it then points towards men, but that would be because they have used it in a form of encounter where men usually were the main warmonger in war.
If people at the club feel that it needs to be changed, then it need to be raised. I can understand some people think it needs to be changed, and I can see why others, usually classed as the old guard or whatever don't, but is that because the name of the club has been around for many years, when it may have been perceived as men only, even though you see pictures from many years ago with women taking part. The sites I have been on that have Bowman in the name have pictures that have women shooting at the club, so doesn't show that its men only.
Maybe if it was raised with AGB or similar with the majority supporting the change, then it needs to be pushed for.