Carving is going to be moved into the new crafting systems as shaping sometime soon, but for now it works the same way as it always has (for the past 3-4 years..I can't say before that)
I'm not sure how much skill in mechanical lore or bows is needed to make things on the low end.
I worked with a young ranger recently who wanted to make all his own armor and weapons. I believe a few days of bow classes were all he needed to make a bow, but I'm not sure how many ranks.
Before I converted my mechanical lore to outfitting I was able to carve canes. Afterwards I think the best I was able to carve was a sharp stick. That led me to believe that what you carve is based on how much mechanical lore you have..but that's just a guess.
I have one question though..when you are trying to carve a shortbow, are you using just a normal stick you foraged?
If so, you need to forage a stick from a particular type of wood. I believe pine and spruce sticks are the easiest, with alder, apple and ash being just slightly tougher. One of those should be available to forage wherever you happen to be.
You might have already been here or know all the steps, but here's this just in case:
https://elanthipedia.play.net/mediawiki/index.php/FletchingI ended up foraging a pine stick for the young ranger I was helping. He didn't have enough outdoorsmanship to forage one, but he was able to make his own bow from it.
