I tried to pick up the bunny but it ran away
Do you know why it ran away from you?
It probably got scared of me and the possible harm to itself.
Rabbits are wild animals when they are outside and they need to be left alone. You need to respect nature and the animals in nature. It's not fair to disturb them, even if you just want to interact.
It's just a rabbit, man... No biggie.
You're right that it's not a big deal, however, if you still want to interact with rabbits, you could always go to a local animal shelter.  There will be lots of very calm, tame pet rabbits there, and the employees would probably love it if you just spent some time with them, to save the animals from loneliness.