I'm not a pilot but I see that you haven't gotten a response yet so I'll throw in about as much as I know from just having general aviation interest.
There is something called CAT (clear air turbulence), like as the name implies, are disturbances in the air in clear weather and is not visible on radar or to the naked eye via cues like cloud formations, so it is difficult to impossible to avoid. There are several degrees of severity of CAT.
Modern airplanes do have weather radar and pilots always navigate around severe storm activity once in the air.
But well before a plane leaves the airport, a flight plan is filed and these flight plans take into account potential weather along the flight route. For example, this is why on a flight from NYC to Orlando you will sometimes see the flight take a more western inland track vs. a track that is out east over the coast. But once a flight is out of their departure area and under own navigation, they are basically following specific airways between different points on the flight plan. So another plane that might have passed along that airway previously would report to air traffic control that there was turbulence, and ATC can then alert other planes on that same route about the turbulence. If it gets uncomfortable enough, pilots can and will ask to deviate up or down (or left and right) to try to get out of it, but there are no guarantees since this kind of turbulence is basically invisible. Sometimes everyone on the plane just has to grin and bear it until it's over and just hope that it doesn't last too long.
So I guess the main summary is that pilots will always do whatever they can to avoid known areas of bad weather (including not taking off in the first place) because bad weather like severe thunderstorm activity is a legitimate danger, but there are some kinds of turbulence that can be uncomfortable and nerve wracking, but is not really a danger to the airplane and is just difficult to impossible to avoid.
Another thing I will say is that I've looked up bumpy flights I've been on on Flightaware and there's basically no change in altitude. So yeah sometimes in a really bad case a plane might hit some kind of downdraft that causes it to lose a bit of altitude in a short period of time that might be felt by passengers, most turbulence is barely impacting the airplane at all even though it feels like it is inside the plane. If you were outside the airplane watching it fly through turbulence it wouldn't even look like it was bouncing around. I am a very nervous flyer but I use the "pretend you're on a bus on a bumpy road" thing and also picture myself looking at the plane from the outside and all those things help me deal with it. So does Xanax, but I like to avoid that kind of stuff whenever possible. Flying more would probably also help - I don't fly very often so it's more difficult to just get used to it.