I got bored and decided to check the code. The tile you're trying to sleep modifies your sleepiness as follows:
Regular Bed + 5
Makeshift Bed, Vehicle Bed, Cot, Sofa or Thick Webbing(With Webwalker Mutation) +4
Rollmat, Fur Rollmat, Armchair, Improvised Shelter or Vehicle Seat(Any) +3
Straw Bad, Hay, or Tatami +2
Floor, Waxed Floor, or any Carpet +1
Having the Chloromorphosis mutation gives a +10 on dirt, dirt mounds, pits and shallow pits. You get a +5 on grass. Anywhere else, including vehicles and furniture, gives a -999, so basically impossible.
Having the web weaver or web spinner mutation gives you a +10 on thick web and a -999 everywhere else.
Not having any of those things present imposes a penalty on your sleepiness equal to the move cost of the tile you're on. So the most important thing is making sure you have anything to sleep on, and the difference between a vehicle bed is only 1 point, +4 vs +3.