Hi, Lou,
I assume that you have had your westie bitch checked out by your vet to make sure that there are no physical problems? You do not say how long she has had this problem. If it has always been there, maybe she has a persistent leak of urine which she wants to keep cleaning up.
Did it start after the last time she was in season? If so, maybe she has a chronic uterine discharge which she needs to keep cleaning up.
It may be a behavioural problem - maybe she knows that when she licks herself she gets your attention, which is a 'reward'!
There are so many things to consider I can only suggest a few alternatives. She will need a complete 'work-up' to reach a specific diagnosis.
Walter