Can I set up a buy x get y (BXGY) discount?

Yes, BXGY is supported by the discount code mode. You can pair a bundle with a Shopify discount code

It depends on whether the "Get Y" collection is the same as the "Buy X" collection

1. X and Y are different collections
   For example, buy 2 T-shirts, get 1 free hat. You can set up 2 bundle conditions. The 1st one is to select any 2 from the T-shirt collection. The 2nd one is to select any 1 from the hat collection. Then you can set the discount like below:
2. X and Y are from the same collection
   For example, buy 3 T-shirts for 2. You can set up 1 bundle condition like buy 3 from the T-shirt collection. Then you can set the discount like below:
   

Then you will create the discount code in the Shopify discount admin. Currently, BYOB cannot create a discount automatically.

Here's a sample BXGY bundle you can try.