Hello Kirsty,
A question - do you have a copy of your grandmothers birth certificate?
If so, it should give both parents name and mothers maiden name and when and where they married.
Unfortunately tips are as only good as the people that give them and are no substitute for documented facts :O) which you're well aware of.....
The offical govt website at
www.scotlandspeople.gov.uk is where you need to start. It's free to register, but costs to download copies - not transcripts.
Min. spend £6.00 which buys 30 credits - allows for the download of up to 5 bmds or census records.
I'd have done a search but am already over budget and out of credits for the month.
A quick look on SP shows that there are only 2 marriages in all of Scotland from 1910 to 1930 for a couple with the name of James Bruce and Mary Smith (entering the middle name of Jane) brings up no hits. So, one of these 2 couples should be who you're looking for. The marriage entry will bring up both parents names and fathers occs. as well as mothers maiden name- address at the time and any witnesses etc.
Unfortunately you can only download birth entries up until 1910 - so if you wanted to be 100% certain about Graces birth and didn't have the cert you'd have to send for it - or if a kind soul was going to a Registrars to do research of their own they could do the look up to confirm parents marriage for you.
So, over to a kind soul heading for a Registrars office.
Regards, Steve

As a matter of interest, in all of Scotland 1920 to 1930 there are 9 Grace Bruces born, only one in 1927 though.
-+