I think earliest you can get this when you reach racer level 12 and unlock Lamborghini Murciélago LP 640. I used it on tier 4 event Causing Offence, but it should work on any event with Overdrive skill. Gather full nitro and wait for Overdrive to load. Then find nice and long straight and use Overdrive to get speed up. Right after when overdrive depletes, use your full nitro. If you had decent speed when entering straight, you should have no problem reching 250Mph.
If you are struggling to get enough speed, go for bounty in other races and come back with faster car.