Hey Zeef I did a bit of digging and the most I can come up with is -
Register on the Bit developer portal, POST some details to their API (I assume your wallet details and an amount) and it will return both a link and a QR code that you can send via whatever means you want.
"Note: The Bit API is governed by Bank Hapoalim’s licensing and is intended for businesses or licensed PISPs—there is no public-consumer P2P API."
Alternatively services such as Grow, Hyp and Upay offer REST interfaces that do the same without you having to go through so much hassle as you do with a Bit developer account.