Whenever I attempt riding up a driveway curb or over a speed bump or any kind of bump for that matter, I fall forward off the uni. Any advice on how to ride over significant bumps?
Putting all your weight on the pedals might help, and throw the uni forwards so your center of gravity is behind you so when you hit the bump your enertial can cary you over it and you don’t fall off (hard to explain).
Other than that Just practice.
As for riding up a curb I can’t and I don’t think many people do, unless they have 24" or larger tires, we hop up them.
I had a hard time with this too. I just worked my way up to it. Start with little places where maybe a section of sidewalk has shifted up by an inch or two, then do bumps a little bit bigger until you get over them. Eventually you’ll be able to ride over curbs.
I can bash my way up 8" on my trials uni. Lean back, put one powerful pedal stroke and hope for the best.
Yes you can roll curbs on a 24", but it just adds a big bumb which is relacable by a clean hop
Practice riding up steep hills. Get to the point that you can float on the pedals going up steep hills rather than feeling like you’re really heavy on the uni. That technique of dancing on the pedals while climbing and lightening the uni will help get you over curbs.
I can bump over a square, non-mountable curb on a twenty. I do as so:
Hold on to your handle,
Put your wieght on the seat
lean back a little so your tire hits the curb before you do
let yourself be thrown forward by your own momentum
swing free arm to recover
ride away.
Note go as fast as possible and keep peddiling the whole time
if you can hop it helps…all i started doing was hop over small things till i could hop on and off curbs…just start small and get bigger…
Do it like Joe2005 said. And think about why you fell, and then change the way you ride up it so you will not crash. Compensate, regenerate, participate. 
But mainly practice riding and all your skills will start progressing so you can do lots of things.
Could someone try to clarify what Joe2005 means by “throw the unicycle forwards”?
You want to get the wheel out in front of you a little bit. Speed up your pedaling without leaning forward, and then keep pedaling and correct your lean as you hit the obstacle.
For me i just lean back a little bit, and speed up, by the time you are on the top of the obstacle you should straighten out.
I hope Joe doesn’t mean to just lean back a bit, plow into the curb, and use brute force to get up the curb. That method can work. But it’s also possible to get up a curb with more finesse. Rolling up a curb can be done smoothly.
Lean back a bit as you approach the curb so you’re at the back of the balance envelope. As you come in contact with the curb take a big step up like you’re stepping up a big stair step and unweight the unicycle. Your forward and upward momentum will let you roll up the curb. I try to think like I’m stepping up a curb that is two or three times the height. That gets me to do the upward body weight shift and unweighting. If all goes right I end up rolling up the curb (I mess it up more times than not though). It does depend on pedal position and timing and weight transfer.
Yeah that’s what I meant to say.
I need to work on expressing myself through words.