The 1911 had a short grip safety and hammer bite was an issue. The 1911A1 has a longer grip safety to help minimize, or eliminate that issue.
I've never been bit by either of mine, the 1911 (Colt made in 1917) or the later models with the longer tang on the back of the grip safety.
Maybe it's my grip, maybe it's my hand.
I do have beaver tail grip safeties on a couple of mine though.
You can install one yourself, but be aware that some brands are contoured to fit perfectly on the 1911's and some require the frame to be machined (or carefully filed/stoned) to make the frame fit the grip safety. I can't tell you the brands that fit without needing a change to the frame but the vendor you order/buy one from should be able to. Brownell's sells them (as do other parts vendors).
Good luck with it.