I'm thinking of running this game but have been burnt by rng in the past. I know there's a bit of rng in this game but does bad rng waste much time?

I think the largest source of RNG is the Old Mine Road section of the game. On a fast run, you'd enter that section before 5 minutes has elapsed on the timer, and you'll have a good idea of whether it's going well or poorly very soon after entering. A bad Old Mine Road is definitely a reset when pushing for a PB.

So if you're OK with the first 5 minutes of your attempt potentially being wasted, then you'll find the RNG acceptable. Otherwise, you'll find it to be too punishing.

Next up, there is RNG when using bunnies to clear the minefield and enter the Vultures' hideout, approximately 8 minutes into the run. The run will be faster if less bunnies explode (less inventory menuing for another bunny, etc.) and they take a direct path (no sidestepping).

Honestly, I've never timed the difference between, say, 6 bunny explosions (a very high amount) and only like 2 explosions (very low), so I can't really speak to how big a factor they are. I at least haven't reset because of having to use a lot of bunnies, so that's nice, but it definitely penalizes one's time. I think being fast with your menuing is probably more important. You can see that the top times still have several bunny explosions, so you don't NEED perfect RNG on them to have a competitive attempt.

That's a big distinction compared to the Old Mine Road, where you really do need to skip very few bikers, plus complete your objectives within 2 laps, if you want a competitive time.

There is some RNG with the very first bunny as well -- the one you unleash on the minefield to be blown up and drop the battery needed for the RC car. If it explodes on its first or second step, that's much faster than if it keeps going -- I've had the thing get lucky and take around 8 steps before hitting a mine and giving me the battery! That takes forever compared to an early mine hit.

That bit of RNG can be avoided altogether though: just place the bunny, and then leave the screen to go back to outside Corely Motors HQ. You'll hear it explode right away. Immediately revisit the minefield, and you'll find the battery there. Thanks to Bigmanjapan for telling me about that one. I like forcing the explosion by leaving, even though the travel time costs you some time, because at least that is consistent. If the battery bunny explodes quickly, it's faster than leaving and coming back. But if you wait on the bunny and it decides to walk for awhile before exploding... well, it's a gamble every time. I like avoiding that bit of RNG.

I think those are the only random elements in the run.

Basically what Prolix said.

If you aim at the first place, then being burnout is definitely a possibility here.