I can sympathise. I have daughters (thankfully 18 and 21 now) but I learned very early on not to make promises I couldn't keep. There's nothing worse than going back on something and then seeing the hurt look in a little girl's eyes. Throw in a quivering lip and you could easily rip your own heart out.
Just remember that she made you make that promise because she wants to have you around for a lot longer ... she didn't do it to deny you of pleasure.
If you can't keep your promise ... just tell her it makes you very sad not to be able to ride and that if you promise to be very very careful, you would like to get another bike. If you can keep your promise, don't worry. There will always be bikes around in the future and when the time is right ... jump back in.
Funny thing is that while my eldest was horrified of me getting a "two wheeled death machine" (her words) I convinced her to go on the back a couple of times and now she'll find any excuse for me to take her somewhere on the bike instead of the car. So, perhaps you could borrow a scooter and a few rides around the back yard with her might convince little miss four that perhaps bikes are pretty cool.
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