I have bow legs and I’m running 5 KM once a week for over a year now. I saw in several websites that running with bow legs might cause problems and saw someone mentioning “under-pronation” which I wasn’t sure what it was so here are a few resources I found that talk about bow legs and running in general:

I use Nike Air mostly and New Balance for running, and I really like both of them.
New Balance WR1224 (Women's) - Silver/Azalea New Balance WR1225 (Women's) - White/Blue
adidas adiStar Ride 2 (Women's) - Running White/Dark Steel Metallic/Art Red adidas Supernova Sequence 2 (Women's) - Running White/Dark Steel Metallic/Art Green
– Shelley