To actually do this, will require a pretty decent stretch of road. A closed track is my recommendation. However not everyone has a track they can use. Ideally with a few helpers. One behind you, one at the end of your run, and one cruising the other direction. Looking for traffic and PoPo, and all being able to communicate with one another. You have lots and lots of open roads out in your desert, just find a place less traveled. Find one that has no or few side roads to preclude traffic entering onto it. If it has sides roads, have a helper at these to advise of any side entering traffic.
I promise, you will eat up a LOT of road at these speeds. You have to look at what is a half mile ahead to prepare for it, because that will be upon you in no time.
It won't take long to hit top speed, but its hard to find a road that you can do it on. 187mph is basically a football field a second.
Yes you can do it by yourself, but be advised, you will probably end up in jail if you get spotted and you stop. If you don't stop you better have somewhere to go. Otherwise you may need Z rated tires to find the next state.