The bags I got a couple of years ago aren't working out.  One them won't lock at all any more due to being rusted out, and the other one locks, but even I can just pull it open despite it being locked.  Found that out today when I went to unlock and open it.  Turned out it was unlocked, so I wound up locking it and then opening it.  Just felt like the Velcro was more tenacious than normal.  Popped right open.  I need a secure bag I can soft mount but trust to leave my purse in.  Is there such a thing?

If you had a purse with  a shoulder strap,you could carry it away from the bike,the fact that you don't tells me you don't really need it ,if so leave it home not in the bike. You could just buy a women wallet ,and put it in your pocket ,after all we have man purses !