msincredible
Mama bike
Sounds like the OP should take her current bike to a track school if afraid of leaning.
Learning how to corner correctly is a vital piece of knowledge to have in your bag of survival tricks.
I got the impression she meant having the bike leaned while stopped.
One thing you might consider is to practice, on your current bike, the art of one-flat-foot-down, other foot up, bike leaned over. This is a really good technique for the short-legged, and will greatly increase both the number of bikes you can ride right from the get-go, and your confidence on all bikes. It may be easier to get comfortable doing that on the bike you're already comfortable on - then you have a skill you can take to any bike. You can tweak a bike to fit you, for sure, but it's so limiting to have to cross bikes off of your list on the basis of seat height alone.
It seems counter-intuitive, but having the bike leaned over a bit is actually more stable. When it's straight up and down, it's a bit precarious, and wants to lean randomly to one side or the other. When it's leaned to the left, it stays that way, and your leg is in control.
Another option is to slide your butt off to the side that you have your foot down on. Then you can have one foot down, one foot up, bike more upright. How much lean is comfy depends on bike weight and center of gravity and rider leg length and strength.
na im kiddin dont get one if you dont want to be hated