Situation: Bound with rope and unable to break themselves free. They then inch-worm or roll themselves down the hallway.
Or are you totally helpless and can't spend a full round to crawl. Note: the ropes are not anchored to anything.
I think by RAW they couldn't move.
I'd probably allow as much as 5 ft. per round depending on whether they can roll and how bound they are. If they're tightly bound like a fat worm, probably more like 5 ft. per minute (10 rounds).
I removed a vulgar post.
There are no degrees of being bound in PF, which makes sense. However, there are these degrees in real life. A person could have only their hands and feet bound (and also their fingers, if a spellcaster), or all the way up to gags, chains, blindfolds and hogties to keep their limbs immobile.
In the first situation, I'd say with supreme effort you could get yourself moving along at 5ft a round, especially if you have room to roll.
At the other end of the extreme, where your captors have taken no chances, I would posit that it would be extremely difficult to move at all, nevermind moving yourself in a specific direction.
So really it depends on the storytelling of the GM and players at this point -- just how well are they bound?
The question I would ask is: could this be done in a movie? If yes, then as GM I would probably allow it, although perhaps at a 5ft speed.
But I probably would have a saving throw of the bound characters Reflex versus 10 + the will save modifier of the person tying the bound character up. If the character tying the bound character up has ranks in Escape Artist, I'd use the number of ranks if this is higher than the Will Save modifier.
I probably would end up making a ruling like this on the fly. For a character bound but not secured to a heavy object, I'd probably allow crawling with a Reflex Save vs some reasonable DC. If a PC is doing the binding, I'd ask the PC doing the binding to write down on an index card how she was securing the prisoner, and use that as a basis for making my decisions.
If you follow the RAW strictly, the answer is unequivocal: NO.
"Helpless: A helpless character is paralyzed, held, bound, sleeping, unconscious, or otherwise completely at an opponent's mercy. A helpless target is treated as having a Dexterity of 0 (–5 modifier). Melee attacks against a helpless target get a +4 bonus (equivalent to attacking a prone target). Ranged attacks get no special bonus against helpless targets. Rogues can sneak attack helpless targets."
The only time you treat your Dexterity as 0 is when you are wholly unable to move under your own power. As such, I would rule that crawling while helpless is completely out of the question.
However, being tied up doesn't necessarily make you helpless.
"Tie Up: If you have your target pinned, otherwise restrained, or unconscious, you can use rope to tie him up. This works like a pin effect, but the DC to escape the bonds is equal to 20 + your Combat Maneuver Bonus (instead of your CMD). The ropes do not need to make a check every round to maintain the pin. If you are grappling the target, you can attempt to tie him up in ropes, but doing so requires a combat maneuver check at a –10 penalty. If the DC to escape from these bindings is higher than 20 + the target's CMB, the target cannot escape from the bonds, even with a natural 20 on the check."
A tied up person seems to be pinned rather than helpless. Even if true, the pin condition specifically states that you cannot move.
"Pinned: A pinned creature is tightly bound and can take few actions. A pinned creature cannot move and is flat-footed. A pinned character also takes an additional –4 penalty to his Armor Class. A pinned creature is limited in the actions that it can take. A pinned creature can always attempt to free itself, usually through a combat maneuver check or Escape Artist check. A pinned creature can take verbal and mental actions, but cannot cast any spells that require a somatic or material component. A pinned character who attempts to cast a spell must make a concentration check (DC 10 + grappler's CMB + spell level) or lose the spell. Pinned is a more severe version of grappled, and their effects do not stack."
So yeah...when it comes to moving about a tied up person is screwed regardless of one's interpretation of the RAW.