Yes, using a bed will restore your whole health same think when you travel by boat. Alcohol as well, some have effect like food ration (health regenerate little by little) and some will act as health potions and restore a whole chunk of your health.
If you choose voodoo later on you'll get a companion that can cast heal. And at the max rank in toughness you'll unlock a regeneration skill that will let you permanently regenerate health. Those are the only options available to regenerate health.
Btw, you can also give some Grog to your companion, those aren't considered as gifts (as in, to improve your relationship with them) as in some others RPGs, they'll simply use them to stay alive in fights.
Provisions regenerate 20 blood over time, well suited while running around or between fights.
Grog restores 50 blood, Rum restores 100 blood. Both of these are immediate and very well suited for use while fighting.
The only time you regenerate for free is when sleeping, traveling on your ship or once you get a skill that requires level 10 toughness. You will have to start eating / drinking, there's no way around it. Get all the tools (bone saw, knife, etc) and kill / harvest everything you run past. You should never be hurting for food.