A bowyer is the person who builds the bows used in archery. Is there a single word (verb/ noun) describing this occupation (= making bows)? Maybe I am a spoiled German speaker, because in German, if there is a word for a thing (Bogen = bow) you virtually always construct a single (composite-) word describing the occupation of making it (Bogenbau).
The occupation would be bow making, plain and simple.
You can spell it bowmaking if you insist, but you don't have to. For all intents and purposes, it is a single word either way.
Never worry about spaces. A compound is a compound. The Germans just leave out a couple spaces, but other than that, it's actually the exact same thing as in English, another Germanic language. It's all about orthography (which is always an approximation and a compromise, by design), but the underlying mechanisms are exactly the same. The German Kontrollflußgraphvisualisierungssoftware is the exact same thing as its English counterpart, "control flow graph visualization software". The exact same compound, part for part, in the exact same order. A single unit, give or take any number of spaces. Spoken language is primary, and there are no spaces in there. They're just smoke and mirrors.