Joanna Perrens is now receiving a course of post-exposure vaccinations.
She was bitten at the weekend as she approached an injured Daubenton's bat on Inchconnachan island.
Bats are known to carry the rabies virus. In 2002 a man from Angus died from contracting rabies as a result of a bat bite.
Ms Perrens was bitten on her thumb as she tried to remove the injured animal after it flew up onto her shirt.
She said: "I really didn't think anything of it - it was a tiny pin-prick of a bite with a tiny bit of blood and we just put antiseptic on it."
She said it was only after talking to a doctor friend that she got in touch with NHS 24 who sent her to A&E. Doctors there established the rabies risk and she was started on treatment.
"It's a low risk that I would have had rabies, but if I did have it then this is obviously 100% effective, so I'm not worried," Ms Perrens added.
"The worrying thing is if I'd gone along as I was - thinking nothing was wrong, it was a tiny wound, and nothing to worry about."
Daubenton's is a common species in Scotland and some of the bats are known to carry the rabies virus.
In 2002 David Macrae, a conservation worker from Angus, died after contracting rabies from a bat.
Since then tests have revealed that 3% of Daubenton's bats have been exposed to the rabies virus.
Bats are particularly active at this time, as young bats leave the roost to search for insects.
Anne Youngman, from the Bat Conservation Trust, said: "It's unusual for a bat to bite somebody, I expect it flew up from the ground because it was trying to escape.
"We know that some of our bats do carry rabies - it's a tiny, tiny proportion but because it's such a serious disease we advise people not to take any chances."
Ms Youngman said that if anyone comes across a bat which looks injured, take care, try to cover it and phone the trust.
The organisation's bat helpline number is 0845 1300 228.
Experts have warned the public to keep their distance from bats after a woman was bitten by one on a visit to Loch Lomond.