You should keep your meter in a separate bag. You can buy those canvas shaving bags online that you can take the meter out of and shove it back into when doing chores that require you to use the meter a lot. That way leads dont get tangled up and the meter is at least not getting knocked around against the tools. The bag gives some protection and its easy to get the meter and the loose leads into and out of as you are using the meter during your routine.
I would never just drop a meter into a bag of tools...... they get nicked up and the leads are in danger of getting nicked up too.... and nicks in the leads can lead to you getting shocked.