Can someone tell me if there is a 3-position safety which can be fitted to this action? Picked one up in .222 Rem and like it, but the factory safety is not intuitive to me. Thanks

Posting pictures would go a long way to helping identify what you have.

"BSA" covers a lot of ground and could be a number of different systems and modified versions of systems.

Presuming the BSA you have is the short action Hunter model but all the BSA Hunters, Viscounts, Majestics, CF2's, etc., all had the same two position thumb safety on the bolt shroud rotating back and down for safe, forward for fire. What is lacking in intuition with that?
With respect there are a multitude of different safeties out there on a multitude of firearms, just have to learn to use each one intuitively as it comes.