Personally, I think it is way too dangerous to let cats outside. If she is bored, you could make her indoor environment more interesting by playing with her more, getting her different toys, catnip, cat trees, etc. If a child was bored playing in the fenced in backyard, I would hope you would make the yard more interesting, rather than open the gate and let him/her roam the neighborhood. I don't mean to be accusatory, but you seem to really care about your cat's saftey, and I applaud you for asking for suggestions rather than just opening the door because thats the easiest thing to do.
If you really want your cat to be outdoors, you could look into cat fencing that would keep her in the back yard, or walk her on a leash like you have done. If other people think that is strange, so what. You are being a responsible pet owner, and that is way more important.