I would rub the problem areas with an alcohol saturated paper towel. If the bumps still remain, they are probably just some harmless areas of oedema.

It could be normal like the poster above mentioned, but if its not my best guess is white flies. My dad had a wax plant that he severely neglected and it had an infestation of white flies. There were fuzzy white things all over it, some large and some small. If this is the case simply wipe the leaves and spray the leaves with a mixture of neem oil, dish soap and water once every 2-4 weeks until it is completely gone.

Those little bumps are not whitefly.

Auron. When a plant has whitefly, when touched or brushed against, whitefly take off..They're quite fast.
Sounds like your dads Wax Begonia had Mealy Bugs.

I agree with Odyssey. If bumps don't wash/rub off, they're not insects.
To be sure, check leaves daily. See if bumps move or grow. Toni

Thanks for the input, folks.

My Jasmine's growth has really taken off and all of the new leaves have that as well. Rubbing alcohol does nothing to this bumps, so I leave them alone. Nothing comes off, nothing moves. The stems have similar hairs so I'm assuming nothing is afoul.