The usual way to do this is to keep your score in Binary Coded Decimal format, or BCD for short.
The 6507/6502 has a native BCD mode that you just need to turn on (SED) when adding or subtracting from the score, and turn off (CLD) when you're done. When it's enabled, for example, if a score byte is $09 and you add 1 it will become $10 instead of $0A.
Using BCD, extracting the lower digit is just a matter of an "AND #$0f" and extracting the higher digit is just a matter of 4 "LSR"s. Rinse and repeat for any other score digits you may have.
Thanks very much for such a quick response. I can see how it would be quite easy (in Atari 2600 terms where nothing is that easy) to do it now. Thanks again.