You can hack up a quick release camera tripod mount using a discarded bike light quick release mount and a 1/4″ bolt, or you can buy this ready made Minoura Camera Mount.
I don’t know if it will hold up to the weight of a full sized DSLR while your bike is bouncing over stairs and potholes, but the quick release looks beefy enough for smaller point-and-shoots.
More about this at SOMAfeed, which says to contact your LBS for price and availability. Suggested retail is $24.95.
(Or you can buy online. There’s a 22-29mm size and a 28-35 mm. The “standard” handlebar diameters historically ranged from 22mm to 26mm at the stem, depending on the style of bikes you use. Newer “oversized” bars range from 25.4mm to 31.8 mm. )
H/T – Andy.