I've used the bit of box I've cut out for the next as a bridge a few times, which works nicely if your using a thicker wood box.
I gotten a little lazy with bridges/saddles lately-I just set a 3/16 brass bolt on a piece of scrap oak(to match my equally lazy nut) and call it a day. Since I prefer light gauge banjo string over even Aquila strings these days I don't have to worry about string wear on the brass-but you might.
You are welcome. One thing I forgot to mention is soundboard bracing. Depending how your neck is attached, you will most likely need some bracing. I have built 3 ukes and they all require bracing. The one in the photo has the neck going through the front and then attached to the top and cut off before the sound hole. Or you might use the Gitty uke neck "kit". and attach it to the front of the box. That works well also. In that you would probably put bracing between the front and the bottom to spread the stress and keep the front from collapsing.
If you brace the top, don't overdo it or you will murder the sound. I like to use the "humidor" thin plywood that comes in most cigar boxes. Put it on edge, glue it well. 2 longitudinal strips should do it. Keep the height to around 3/8"..Even a small uke has plenty of string tension trying to buckle the soundboard.