Yes, it is called Scotland's People. You can get copies of bmd's from there. However, given the person you are researching was born in 1955, you wont be able to view her certificate online and will need to Order a copy.
They also have Census records, some Wills and some parish records.
SP operates a credit system, you can buy them in rising groups of £6. I think it costs one credit to view each page of a search and 5 credits to actually look at an entry.
It's a very good site.