Most luthiers will tell you to NEVER EVER EVER use superglue or crazy glue, but instead either one of the variants of Titebond, or hide glue, and you may get away with Elmer's 'Wood Glue' or 'Craft Glue' but a 48 hr drying/curing time is what I have used in the past to repair my own instruments.
I taped off around the bridge area, sanded all the old glue off both the bottom of the bridge and top of the soundboard, then put a copious amount of glue in each, spread with a fingertip, then set the bridge in place and then put a stack of 5-6 encyclopedias on top and any glue that squeezed out, I removed with a dozen or so q-tips and then one pass with a damp paper towel around the edge of the bridge, and let it sit.
You need to put the books on top before the wiping off the squeeze-out, otherwise you will do the wiping at least twice.
During the time after stacking the books and wiping, you can verify correct placement of the bridge, otherwise your intonation will be messed up, and a 3mm wide saddle can only do so much to fix intonation issues...
The Titebond and Hide glues can both hold a bridge in place on a soprano (~13.75" scale) which usually has no more than about 27 lbs total string tension, AS WELL AS on sizes up to a baritone (~20" scale) which usually has no more than about 55 lbs of total string tension. Classical guitars have the bridges held on with nothing but hide glue for hundreds of years at a 25" scale length and about 100 lbs of string tension.
The briidge does not usually come off solely from glue failure, but due to the fact that the bridge and soundboard are made of different woods, which react differently to humidity, and thus will contract and expand based upon relative moisture content, this disproportionate wood reaction is what leads to the glue being released, NOT the bonding strength of the glue itself. Super/crazy-glue is likely to cause MORE damage to the top because the area under the bridge cannot expand or contract much at all now, and the wood around the bridge is more likely to fail, and thus causing a hole where the bridge used to be.
But I am NOT a luthier, and you will get professional advice as per suggested above by jer, by re-posting your question in this section of the forum:
http://forum.ukuleleunderground.com/forumdisplay.php?30-Ukulele-Building-Luthier-s-Lounge
also, there are tons of YouTube videos that demonstrate the procedure, and likely any done that recommend super/crazy-glue are NOT a pro, OR are put up by folks that have not done their research. Using the wrong glue means that you cannot easily remove or repair again if you mess up without extreme damage to the instrument due to the use of acetone solvents to release the super/crazy-glue.
However, it's your instrument, and you are free to do as you wish.
Hope this helps and best of luck