We bought a specific bag as well! 
RyanAir isn’t fooling around with those personal item dimensions, I believe they are 15 x 10 x 8 (inches). RyanAir has a bag slot at each gate D20’s flown out of to measure bags if the gate agent has even the slightest doubt about sizing. And massive penalties to pay if your bag doesn’t fit.
Edited to Add: Here is a bag similar to the one we found for D20 (but we got it on super clearance as a discontinued item). Just to give a frame of reference as to the size we’re talking about.