I'm glad you're getting encouragement to let your DD ride the bus!
My DD is only 4.5, so she doesn't use any form of transportation by herself yet. But our family are heavy users of both bus & bicycle, and it's our goal to have DD confident in using public transportation and her own bike so that she can be very independent by the time she's a teenager, if not sooner.
I do sometimes encounter weird attitudes about public transportation. Once a co-worker was complaining about how she was having a hard time getting to the airport, and I suggested that she take the bus. She said "I don't think so" with a look on her face as if I had just suggested she ride a turd to the airport. Our bus system is really quite good, and I was kind of shocked that she had such a negative reaction.
So, it's perhaps good to know how people feel about public transportation in general before putting too much stock in their opinions about your daughter's use of it. I find that the people with the most negative attitude about the bus are often the ones who've never used it.