Like any journey that involves cars and distance, how far you decide to drive is essentially down to you. From our point of view breaking the journey by camping by pyramids makes a lot of sense.
From Khartoum to Meroe takes about 5, or so hours with us breaking up the journey in Shendi. Apparently the police here are a little tetchy, and thus photos are frowned upon, although we snuck a few.
Obviously the main point of Meroe is to see the Pyramids, but it also offers a great place to camp (next to said Pyramids).
Of course, there are towns nearby, and hotel options, but in Sudan in general, and certainly in Bir Tawil, camping is the option.
Our local guides cooked us a great dinner in the desert, and we hunkered down for the night. Day 2 of the journey to Bir Tawil.