A bound character is considered to have the helpless condition and a character with the helpless condition is treated as having an effective 0 in dexterity, meaning that he can't use stealth anyway. So... I don't think he would be able to use it.By this logic, a bound character, being helpless and thus an effective 0 Dex, also can't use Escape Artist to get out of the bindings.
Even if you allow the check, since that's one of the purposes of Escape Artist, do all attempts to get out of ropes have an effective penalty of 5 + Dex modifier for being helpless: Highly dextrous characters are no better than anyone else at escaping bonds?
As a side note, does it really make sense for characters tied up outside of grapples, while unconscious or whatever, to have their escape difficulty based on the binder's CMB? Big, strong creatures are better at tying people up?
Well, a big strong creature can certainly force limbs into uncomfortable and binding positions and pull knots tighter.
It's more weird that part of your BAB is essentially knowledge of tying people up, but honestly, who still wanted "Use Rope(dex)" to be its own skill? At least some arguments can be made for combat proficient entities having experience with binding enemies and more importantly if you know how to grapple, you know bit about how to contort someone with bindings to make it more difficult for them to move/escape.
If you don't like that it's specifically strength based, there are some ways to use dex for CMB instead of str, so you can even work it in non-standard means.
However, if you are personally against it, could always discuss the point with your GM or make your own exceptions if you are a GM. If a sultry seductress with S&M experience argued that she should be able to make an applicable skill or ability check, I'd probably be inclined to agree she knows how to tie somebody up well, if not tightly, so it seems applicable (perhaps replace BAB with an applicable skill modifier or strength with dexterity as in the RAW work-around above).