Most Helpful Guys
I would not approach even if I knew she was not taken. Girls are way to mean to guys approaching them to attempt to try off line is asking to be called a creep.
Unless you are perfectly her type.
I generally don't approach women any more in person, but in my 20s and 30s, unless she had a wedding band, was with her boyfriend, or I knew she was in a relationship, I would approach her if interested. In general, I'd assume she was single unless there was a reason to think she wasn't.
Most Helpful Girl
Most guys hate rejection so they assume most girls they are interested in are taken just so they avoid being rejected