bump-free mecanum wheels

[kamocat]

Yes, you need overlap between your rollers.
I'll use the term "tread width" here to mean the distance (perpendicular to the wheel axis) that the rollers contact the ground when the 'bot is moving forward. On many two-plate designs, this is also the distance between the plates.
If your rollers are at a 45 degree angle, then your roller length is the tread width multiplied by √(2).
I believe determining what angle of the wheel that will cover is an inverse sine function of (tread width)/(wheel radius).
So take 360 divided by that angle, and round up. That's how many rollers you need on your wheel.