I wear my glasses under my bucket, but it's a pretty tight fit. I think it depends a little bit on the type of padding you have inside. I use . . . old socks. I know, it's weird. But it was cheap. However, it has a lot of give, so it makes it so I can wear my glasses. So part of it comes down to assembly, part is what size and shape your glasses are, part is how big your head is, and the last part is luck. For me, it was mostly luck. Even so, I have to be pretty tricky when I put the bucket on and take it off. If I don't do it a certain way, then it pulls my glasses off.
Best of luck!