When a character gets injured in say a dungeon and they need time to heal, say 1 week when does that timer start? Can they still ride with the party back to civilization but they still need a full week when you get back? Can they get rest on the road? Do they slow you down when traveling?
On a related note, if a party member gets their arms ripped off by a vampire and needs a month of bed rest, but then gets Restore Life and Limb (or in this case, just Limb) and rolls that they need two weeks of bed rest, are those cumulative or does the new one overwrite the second?
My personal rulings on each of these would be (and I am not an Autarch):
A character’s bed rest only counts when they are actively resting, all day. They cannot ride, but could lay down in a wagon. (If you don’t have a wagon, you could make a travois, or you could make camp in the dangerous wilderness, or you could leave them behind.) They will probably end up slowing down your travel one way or another. Days when traveling, even if lying on a bed in a wagon the whole time, do not count as rest (riding in a wagon while injured is not fun).
I would rule that the effects of RL&L completely override all results of the mortal wound.
The section on “healing” on ACKS 105 tells us that normal HP damage is recovered with “each full day of complete rest in reasonably sanitary conditions”. “Bed rest” to recover from mortal wounds is over and above that requirement - if you get out of bed, then you are, by definition, not on bed rest and it seems reasonable to assume that “reasonably sanitary conditions” are also required. So, no, you don’t get any natural healing at all (neither HP recovery nor bed rest) while in the dungeon. You might be able to get natural healing during travel if you’re riding in an enclosed coach or similar, but not while walking, riding, in a wagon, etc.
ACKS 105 also tells us that characters in need of bed rest “cannot take any action other than speaking and moving at half speed.” So, yes, they would slow you down unless you have a wagon, travois, etc. to carry them, as Aryxymaraki suggested. (But note that the wagon itself may also slow you down…) Personally, I would allow them to ride at half speed, given that the rules state they can walk at half speed and riding is generally easier than walking, but I could see this being ruled either way.
Also note that “If the character is killed again before he has had sufficient rest, he cannot be treated or restored to life by anything less than ritual magic.” (still p.105) While other interpretations are possible, I believe that, in this case, being “killed” means “reduced to 0 HP or less”. Since you can’t go above 1 HP until your bed rest is complete, this means that, if you take any damage before your bed rest is complete, you’re dead. Needing bed rest is serious stuff!
I agree with Aryxymaraki that RL&L completely overrides anything from the mortal wounds table. Erasing mortal wound table results is RL&L’s primary purpose, after all.