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We have some older Bullitts and one brand new one, the only one that I don't notice the front wheel wobbling alarmingly when going at any sort of speed is the older one with the damper. It seems to be less exaggerated when the bike is fully loaded than when it's empty so maybe the weight of the kids is cancelling it out. To be honest, I've never had anything bad happen because of the wobbly front wheel but I can't imagine it's a good thing!
ltc-
At low speed the wobble is because the front wheel is almost unloaded(front braking unloaded is always scary),imperfections in tires and steering tolances make it worst
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Things get more rattly on an empty bike, but even that hasn't bothered me. I'm a casual rider, so maybe that's a part of it, but I actually quite like how Bullitt handles.
aka
paradroid
My Bullitt use is mainly leisurely weekend rides with two kids, but I haven't really had any issues with steering. This is a newer model with tapered headtube and fork, not sure if that makes any difference.
There is some play in the steering, I suppose that's unavoidable with a steering rod. I've experienced some judder when descending fast on rough asphalt, or briefly when going over bumps at speed, but I've felt it's predictable and not something I have to pay much attention to.