Quick tips to avoid resting in the private room (and therefore advancing time).
How to Not Sleep
Use vehicles as much as possible
It’s important to stress that maximizing vehicle usage minimizes the amount of wear you put on your boots, your equipment (if in a truck/going through timefall), and your maximum stamina. Despite the game saying the truck has a difficult time going everywhere, once you get used to how it slides on inclines it can be surprisingly all terrain. Also keep the vast majority of your cargo on the vehicle — even with a level 3 power frame, you bleed stamina much faster under any kind of real load. Vehicle jumping, particularly on the trike, can be used to clear some smaller bodies of water or chasms in one go, though a bad jump can cost you your vehicle and cargo.
Avoid (repeatedly) doing BT areas
BT zones are a huge strain on resources (especially on higher difficulties) and threaten BB’s state. You can usually do one or two before putting BB into autotoxemia, but with long enough between BT zone visits you can recover BB’s maximum mood through likes and feats (driving fast, sprinting long distances, double jumping, avoiding falling when you lose balance). Just be fast when looting BT zones, they have a fairly short respawn timer.
One of the biggest things I wanted to mention here that a lot of people may have missed — you don’t have to go to your room (and advance time) or put a vehicle in a garage (and thus unload its cargo) to repair it. Simply customize its paint job (Garage menu -> Customize (F/Y/Triangle)) while it’s on the garage elevator — it’ll get completely repaired, recharged, and still have everything on it. You can even do it while accepting cargo for a mission.
Dealing with problems that arise as quickly as possible is, of course, part of preserving your time-limited resources, so make sure you’re adjusting your equipment loadout to match your goals in game. Taking on a mule base? A sticky gun can help you throw them off balance while giving you a luggage projectile to throw in someone’s face for a quick takedown, bola guns are excellent from the moment you get them right up until the non-lethal rifle is available, and stun grenades take down trucks and everyone on them in one or two tosses — while being quite stealthy at the same time. For BTs, lethal rifles, blood grenades, and even BT handguns (especially when shooting already tagged body parts) — stock up with everything your backpack and pouches can carry if you’re on hard or very hard, though, as it’s entirely possible to run out of resources mid-fight, and relying on other Sams to give you anything to help finish the fight is a risky proposition for both you and BB.
And don’t forget your skeleton, either. A speed skeleton is huge for combat, while power makes looting or general cargo work a breeze.
Bridges, ladders, ropes, chiral bridges (in areas that aren’t adjacent to BTs — they’re all but useless in BT areas with frequent timefall), jump ramps for getting down from cliffs or the tops of steep hills (you/your cargo don’t take fall damage while buffed by one), and especially zip-lines are much better than trying to walk through a river or climb over some rocks. Safehouses and generators strategically placed can also keep you going good and fast — some bends in roads are all but built for generators, as a well placed level 3 can give you a huge amount of charge back without needing to stop, saving valuable seconds on timed deliveries.
Learn where the hot springs are
You’re going to eventually incur fatigue no matter what you do, but a quick dip in any of the game’s hot springs (as long as there’s no timefall) will restore you to full. Also convenient for quickly refilling your no-longer-Monster-brand energy drink. You don’t get the ability to gain the extra 25% stamina from using your private room, but that barely matters as long as you drive everywhere.