I had a similar problem on guitar transitioning from a C to an F (the uke is like starting 5 frets up on the guitar) until someone showed me a trick. Now it works for the Bb on the uke.
( As shown in this link for the guitar, we usually designate our fingers as 1-4 starting w/the index finger & going to the pinkie - Finger numbering
Finger an F chord 2010 & then practice "rolling your hand" so that #1 (your index finger) barre's the E & A strings at the first fret, #2 drops down to the C string, 2nd fret & you "add" finger #3 to the G string, third fret which ends up as 3211.
Practice this "rolling" motion from an F to the Bb (which IS a common transition) & see if that helps. It MAY seem awkward at first, but I found it to be a natural action when I learned it for the guitar many years ago.
Also, you need a proper hand shape with your thumb on the back of the neck, not hooked over the top (I mean you can just about do it with a hooked over thumb, but it's waaaay harder).
And, your first finger isn't flat when it lies across the e and a strings at the first fret. It's rolled onto it's outer side a bit, towards the nut. It's also not straight down behind the 2 frets, but on a bit of a diagonal, closer to the fret on the e and closer to the nut on the a. And all of your fingers can be leaning a bit towards the nut if it helps. Here's a picture on guitar showing it:
It'll take 2 or 3 months to get competent at this, as it's using a whole new set of intrinsic muscles in your hand (they're the little one's between your fingers and in the lumps at the base of your thumb and pinky), and they need time to get into shape. If you find the muscles at the bottom of your thumb are aching, have a rest and maybe massage them, but keep going as you were because you're on the right track.
Good luck, crack this and you're over one of the most difficult hurdles!
Ergonomic tip: It can help to bring your left elbow closer to your body---to play a barré chord, best to have the fingers pointing in the same direction as the frets.
It was easiest for me to barr all the strings on the first fret with my index finger then place the other fingers. I could never get my index to just push down the first two strings cleanly. Hope that helps.
Does anybody just bar the first fret, top to bottom with the index finger, then hit the other two with the middle and ring finger? I guess that was easiest for me and I've been doing it that way. Maybe it isn't such a good idea? I've been doing the B the same way, except a fret over of course.
It was easiest for me to barr all the strings on the first fret with my index finger then place the other fingers. I could never get my index to just push down the first two strings cleanly. Hope that helps.