Have you looked at her marriage record at Scotland's People? It should name bother her parents.
Scotland's People has digitized versions of Scottish civil registration records [not covered by privacy laws] and census returns [1841 to 1911]. It's the only place you can get most of these records. Pay per record, rather than a subscription, but you should be able to get the basic records for not too big an investment.
Her birth record is there as well: born 1886 in the Stevenston registration district. Reference # 615/ 73 for 1886. Searches and the index listing are free, but you definitely want to buy the record, as there will be additional details.
Once you've gotten those records, you should be able to track the family in the census and find the relevant records for her parents. Scotland started civil registration in 1855, so her parents may well have birth records.
Before 1855, you'll need to use church records and the 1841/1851 census returns to go further.
