Telling them to go play or go away or even go inside works... sometimes.

Here's my trick if your bestie is following around too closely and getting in the way:
Click to reveal..
Do this early, before you start your peeps on a civic project but AFTER you've gotten your daily gift. Talk to your bestie near the project your peeps will be working on during the day. Then start the project. It seems to take the three closest peeps as workers, and if your bestie is occupied on the project he or she can't be bothering you. Be sure you get your daily gift first, though!