When I was getting my hair cut, my hairstylist and I got on the subject of ghosts and such. The discussion then turned to Bigfoot and I told her I totally believed in Bigfoot and so did she. Then she said her Mother-in-law had an encounter one time where she was driving down the road and there was a deer rummaging through a garbage can on the side of the road. As soon as she realized that deer usually don't rummage through garbage cans this "thing" looked up at her as she drove by. She will not talk about it...and she supposedly gets freaked out by the image of witnessing it. Anyway, I would love to talk to her and ask her some questions, especially details of where it happened....Im just wondering if it's worth it to pursue and how to go about it....

I would not bother! This lady obviously does not know what it was that she saw.
If she is not ready to talk about it, then you would be doing her 'no' favor for raking it up.

You know...you have to take into consideration other people's feelings. This is something rarely practiced in this field.
At the most you would hear is an intriguing tale about a weird encounter.
The worst would be a woman forced to recognize and analyse what she may, or may not... have encountered!
Unless you have some kind of Phd in this subject..do not play the 'interested party.
Leave it to her relative..if you really must have more information!
But, my point is...sometimes it is better to let sleeping dogs lay...unless you are an expert dog trainer!

If she doesn't want to talk about it with family members I really doubt there's anything you can do to convince her to talk about it with a stranger.

Sometimes talking with a stranger is easier than talking with family members. Of course it always must be their idea to talk, even to a stranger.