What could cause tiny (non-frothy) bubbles in urine which do not burst or disperse easily?

I have no idea. : Probably nothing abnormal. May be some pre-ejaculate remaining in the urethra. If concerned, talk to your doc.

Hard to saydepends,,: Urine has small amounts of protein molecules, excess sodium, potassium, creatinine, and other things that may result in bubbles like this, but it's inconclusive as to what can cause these on a consistent basis. Things like bicarbonate/carbonate, carbon dioxide, carbon monoxide may also do it, but it is rare if ever that these are noted in urine. If you have a health issue see your dr./urologist.