With the help of Wiktionary, we know two useful Midlle English etymologies of the word "bow".
From Old English boga, from Proto-Germanic *bugô. Cognate with Dutch boog, German Bogen, Swedish båge, Danish bue.
From Old English būgan, from Proto-Germanic *beuganan. Cognate with Dutch buigen, German biegen.
And the change from "g" to "w" here is very interesting to me, but I am unfamiliar with the process, even the name of the "sound law".