I had the exact same problem just over two years ago now when i propose to my now Wife. I got hold of a ring sizer from a jewellery store (they give them away free), and i was quite lucky that her Mum was getting remarried, so it would not seem out of the ordinary that her mum would have one of these, so she tried it on and bingo, i got her ring size.
Do you have any sisters, cousins etc that are getting married and would naturally have a ring sizer about? I found that if i left it on the table, whenever my sister, or my wife friends would come over they would just try it on naturally. So maybe leave one lying around.
As a backup, in the lead up to this, (i wasnt sure how i was going to get her ring size) i started making playful jokes that she has chubby fingers (she hasnt) and they're fatter than mine etc. If you keep dropping little jokes, then you can settle it one way or another by comparing each others ring sizes, you can say you were talking to someone at work about your chubby fingers joking with the girlfriend, your colleague is getting married soon and gave you a ring sizer so you could settle the dispute once and for all as she thought it was cruel etc.
Hope that gives you some ideas and good luck
