Have you ever had someone use this phrase on you -- then follow it up with a request that actually does bother you?
Bothers what you were going to do with that $20. Bothers what you would've done with the next 10 minutes of your day. Bothers the fact that you weren't even going to leave the house again today.
Fact: most of the time when you're asking someone for something -- money, time, effort -- your bothering their equilibrium of whatever they were doing before your request. This is true.
Does this mean you should never ask for anything? No. Just stop apologizing for it.
I'm calling you right now because I have something you'll probably want to pay $10 for. Listen up. 
I need a ride to the mall, mom. Please! 
I'm interrupting whatever you were gonna do for the next 30 minutes with this Periscope live stream. I am demanding your attention. 
We only make changes in life when we're bothered. Bothered about being overweigh for the last 6 years, we join a gym. Bothered that we didn't make the team again, we work on our games. Bothered by it being cold in the house, we turn up the heat.
Unbothered people do nothing. If you want to move a person to action, bothering them is the point.