I size the bow and the hide (both mating surfaces) with glue. Doesn't matter if it gels or has a lump or two, but the smoother the easier it will be .
Try hand sanding first.
Your hide should already be stretched from the drying process,so no real need to stretch it on the bow .
If you soak it first, it will try to shrink away on you.
Start in the middle and work a section at a time 4-6"
Iron should be on a low setting. If it sizzles water ,it's too hot.
The heat will reactivate the glue,and while it's still hot,I squeegee the hide on using a small section of polished brass bar.
Keep a little cup of water on hand to lubricate the bar if necessary. use sparingly
The glue will ooze out of the edges and the hide should get transparent. You can see the grain through it.
Don't push too hard and starve the joint of glue.
The hide can be nicely worked into nooks and crannies.and in an hour or so you can slice off the excess with a razor blade.or sharp knife.
Be sure to cut towards the wood so you don't lift the hide.
Save the final sanding /filing until the glue is hard (cured)
No need to touch the back if everything was prepared well. you should now have a nice burnished /glossy finished hide on your bow.
This will NOT be waterproof . cover it with a snake skin, cherry or birch bark ,or lots of a good water tight finish. I used Shelac. Natural,primitive,inexpensive, good colour and found to be the most water resistant by wooden boat magazine!I'm not going to argue.
I prefer the "French polish" method of applying it . (youtube)
This method of applying the hide is the same as Hammer veneering in cabinetry. You can youtube that as well to get some good visuals on glue consistency etc. There is a Bowyer of renown that uses this technique, but I can't remember his name. Some refer to it as his technique but that just somehow doesn't sit right with me as it's been in use for hundreds of years ,not unlike what is now being called the "Perry reflex".
Finished backing should be cured within a couple of days to be safe.