A simple way to measure diameter is to wrap a tape measure around it and get the circumference then divide that by pi.
If you have other bamboo plants at home make sure its sprayed before it goes to your home. Then, even at your place it should be quarantined for awhile to make sure the pest is eliminated.
But in all reality I think most people would not get something that is infested with mites. Is he offering you this bamboo for dirt cheap, otherwise look elsewhere. Dulcis is a common enough species that you shouldn't have to buy one with problems already. Maybe if it was parvifolia, a lot of work would be acceptable.

I had to look up "parvifolia". I thought maybe you were Italian, and "parvifolia" meant free ... I guess parvifolia (Chinese Elm Bonsai?) is extremely rare and valuable. I must also admit to ignorance about pi (3.1415?) I had to ask my stepson, the math whiz. You've got to be a mathematician, or possibly not, but certainly you're running a lot more wattage than I'm burning. You may be right about buying the Sweetshoot elsewhere. But when we see a mature gove, we really want the whole grove, don't we? Some kind of gigantic moving rig is needed, with a scooper big enough to get under a small parking lot. Then a helicopter to pick up the whole grove and lower it into the "mite free" vat - momentarily, before flying it home.

1) You won't be able to grow this bamboo from branch cuttings.
2) You don't want to bring it home unless you can quarantine it and spray it with something that is mite-specific.
3) People who measure their bamboo often use a simple pair of large calipers and take the diameter measurement chest-high.

Why not just get a rhizome, that would be mite-free, wouldn't it? This is a good time of year for it, the boo has plenty of energy stored up. I'm certain that a good rhizome section, particularly one with a growing tip, would grow fine. This is a standard way of propogating running bamboos.