Someone said "Do you want me to wait for you?" I don't want to cause any trouble to her. Which sentence is the most apppropriate?
"Thank you, but you don't have to."
"Don't bother about it."
"Don't bother waiting for me."
Also if there is any difference in the implications between "not bother" and "not have to", could you explain it?
Be careful about "don't bother", it can be interpreted as actively hostile.
It's about like when you say to your other half, "I'm going to spend the rent for the next 3 months on a new motorbike", and she (sorry, it's usually "she" in this context) says "Fine!" when she really does not mean "fine", what she means is "I'm obviously not going to be able to stop you doing whatever immature selfish thing you like, but if you do, then our relationship is over."
In this case, "Don't bother" means "It's obviously far too much trouble for you to just perform this minor courtesy for me, and I clearly cannot rely on you to pull your weight in this relationship, so please be aware that our relationship is on shaky ground as of now."
So if someone offers to wait for you, and you say "Don't bother", it can be interpreted as a rude rejection of a courtesy offered, and the person asking would spend considerable emotional energy wondering what it is that he or she has done to upset you.
Better would be:
"Thanks, but you go on ahead, I'll catch you up later."
Then there is nothing in what you said that indicates that there is any sort of obligation that you need to be waited for.
Even saying "thanks, but you don't have to" is using the language of obligation and duty ("Have to") and can cause awkwardness.
Which ever option you go for, thank your friend for the offer.
In general, "you don't have to" can seem as if you're close to accepting the offer. ("You don't have to, but thanks that would be great.")
On the other hand, "don't bother" can seem a bit negative - it's often used when you're a bit irritated with the other person. ("Oh, don't bother!", walks out, slamming door...)
Maybe the best option would be to thank them, but assure them that you'll be fine.
Logically speaking, You don't have to is a simple statement of fact which your friend is free to act on or ignore at her discretion, while Don't bother is a request that she should specifically not do the indicated action.
In practice, however, there is no functional difference between the statements; Don't bother may be considered more informal, but that's about it.
