They claim the Starr Carr bow is the oldest complete bow found in Europe - it is a little questionable, not the date, I think that has been reliably defined by the articles I have read, but the completeness.
The earliest possible evidence for archery is around 64,000 ybp in the form of stone and bone points. These are probably from a bow but may have been used with some other form of dart or spear.
There is better evidence from 48,000 ybp in Sri Lanka – again these are only tips but the prey were tree dwelling mammals and the tips are too large to be used in blowpipes.
The earliest evidence of a bow is in Europe from around 18,000 to 17,500 ybp. This find is of one limb and the full bow would only have been around 110cm long and made of pine, an unusual bow material. Small bows would normally be used with poison arrows but not in Europe as there are no poisons toxic enough. Note, however, that peat bogs in Europe preserve organic matter better than other environments and older bows from arid and tropical environments will not have survived.