I guess I should mention that after you peel off the back and stick it, you don't really move it. So you can cut off long strips and play with their size/shape aligning next to the last stuck on piece first if you want, then when you think you're good with it peel off the back and secure it in place. It's hard to describe this but when putting two strips together on the bucket, the one going in can be placed almost into the side edge of the next one, such that when you place it down finally you can just apply a bit of pressure with your finger between the two of them and create a fairly seamless join... I guess what I'm getting at is this avoids creating small gaps between your lines.
Another tip is what to do with the very top of the bucket. You really don't cover 100% of the internal with neoprene, maybe go up 80-90% of the height. The very top crown of the bucket will be a small open zone, maybe 4"-6" in diameter depending on how your project went. This is where a nice piece of circular helmet padding finishes up the deal perfectly (and makes for a nice comfort). Generally speaking, step one is lining the helmet with the neoprene, step two is using pads on the top for that part, but also placed around the helmet as needed to create a very snug and secure/comfortable fit.