Green’s Dictionary of Slang

a swindler, a sharper.

1602		Rowlands Greene’s Ghost Haunting Coniecatchers B: These Batfowlers or Conicatchers hauing lost a collop of their liuing [...] inuented a new tricke to fetch in the pence.
1608		Dekker Belman of London G3: A Batfowler walkes vp and downe the streetes, and counterfeits that hee hath let fall a Ring, a Iewell, or a peece of gold, requesting some Prentice, (when there is but one in the shop) to lend him his candle a while, to find his losses.