Bobbin Size on The Machine is so important, that multiple mentions of it are made in The Manual (yes…I am capitalizing like formal nouns. It is that impressive). If the bobbin doesn’t fit, you’re gonna have a bad time This is SO important, they include actual size drawings in the book to compare your bobbin to, to ensure proper sizing and fit for your bobbin.
Baby Lock specifies that part code for the bobbin is X52800-120, which is Class 15 type bobbin, so yes, you CAN buy generic brand, but make sure it is Class 15. And CHECK IT against the picture handily provided in The Manual.