What is the difference between I don't wanna bother you
and I don't wanna disturb you
and I don't wanna take your time ?Feel free to just provide example sentences.

@lqo10 Meaning
Bother-1.to disturb, annoy or worry somebody
2.to make the effort to do something; to spend time and/or energy doing something
Noun-trouble or difficulty
Disturb-1.to interrupt somebody while he/she is doing something or sleeping; to spoil a peaceful situation
2. to cause somebody to worry
3. to move something or change its position
Take your time-1.It suggests that the person you're talking to is busy and their time is valuable.
2. to do something without hurrying
So,as you can see there is no such difference between them