It looks like your second half of the question didn't come through, but I was able to see it. I've gone to our warehouse and was able to fit the caster insert over the 35108 mop bucket caster. The fit was very snug, but did make the caster attachment stem larger. The caster insert is just over 1/2 inch in diameter.
Without having the product number of the caster you purchased I can't be sure this Continental Manufacturing Caster Insert will fit. It is meant to function as you've outlined, making smaller caster attachments fit larger holes, but unfortunately I can't be positive regarding your specific caster.
If you can get back to us with the product number of your caster we'll be more than happy to help you find the piece that will make it work for you!
If you're positive you have the Wave Brake model, then you need the caster I'm attaching below. It does not require an insert. If you have a different bucket, please call our sales team at 888 388 6372 x2 so we can figure out what casters/inserts you need.