Let's assume she made x batches of biscuits.
Each batch makes 75 biscuits, so she made a total of 75x biscuits.
Her friend gave her an additional 60 biscuits.
The total number of biscuits she had for the bake sale is 75x + 60.
Setting this equal to 360, we have:
75x + 60 = 360
Subtracting 60 from both sides, we get:
75x = 300
Dividing both sides by 75, we get:
x = 4
So, she made 4 batches of biscuits. Answer: \boxed{4}.