Keep trying! I bet you can get more of them.

Check Here: https://www.mariowiki.com/Mario_Kart:_Double_Dash!!
The Bullet Blaster has the worst "Medium Off-Road" Stats in the games tied with Koopa King, which also can't make it.

I did some random calculations. I figure that we get the mini turbo frames at the top speed value then the rest at the Medium Off Road value. I chose 200 frames as the time to cross the grass as the values it gave were mostly right.

So the Formula I came up with was (200-MiniTurboframes)*MediumOffroad+MiniTurboFrames*TopSpeed
Probably not the most accurate, but it seems like an okay start.  

Kart	TopSpeed	MediumOffRoad	MiniTurbo	Score
Koopa King	144	68	10	14360
DK Jumbo	143	71	10	14920
Wario Car	142	74	10	15480
Bullet Blaster	143	68	30	15850
Red Fire	140	74	20	16120
Bloom Coach	141	77	20	16680
Turbo Birdo	141	77	20	16680
Green Fire	142	77	20	16700
Parade Kart	142	74	30	16840
Turbo Yoshi	139	80	20	17180
Heart Coach	139	83	20	17720
Piranha Pipes	143	86	10	17770
Boo Pipes	137	92	10	18850
Barrel Train	143	86	30	18910
Para-Wing	136	89	30	19210
Koopa Dasher	137	89	30	19240
Waluigi Racer	140	92	20	19360
Goo-Goo Buggy	136	92	30	19720
Toadette Kart	136	92	30	19720
Rattle Buggy	137	92	30	19750
Toad Kart	138	92	30	19780

So this gives us a rough estimate of how hard it should be to jump the well with each kart. Scores of less then 18000 are challenging, and scores less than 16000 may not be able to do it at all, and for the most part it seems to line up with your experience.

The only question is why the Parade Kart is so difficult with such a high score. It seems like it should make the jump better than Red Fire at the very least. It has Better Top Speed, Better Light Offroad, the same Medium Offroad, better MiniTurbo, the same acceleration, and higher weight. If the weight was a big factor you'd think the Pipe Karts would struggle more, and the bullet blaster would be one of the easiest. Oh well, maybe a true MKDD scientist can tell me where I'm wrong.