I leaned, halachically since nowadays we are doing the mitzvah for other reasons, it does not have to be in a hefker place, if you think you will never be able to do this mitzvah again.
It used to be people would eat the birds, and therefore it would have to be in a hefker place. In some places it is so hard for this mitzvah to come by, we are supposed to go according to the most lenient psak, which means in this case you would not have to make the area hefker.
What it means when it says you have to chance upon it is: you cannot raise birds to lay eggs and then do the mitzvah of shiluach hakan. It has to be just found.
Just a tip: make sure it’s the mother that your shooing away and not the father, otherwise you’re not yotzei the mitzvah. Some birds like the dove and pigeon to be exact, the father lays on them during the day, and the mother only comes at night.
I hope I was of help to you, and if you have any other questions I will be happy to assist you if I can. (We learned these halachos in Great depth.) Tizku Lmitzvos.