Your Bernina has adjustable upper and lower tensions. These can be adjusted to work with any thread. Some people are afraid to adjust their tensions. Just remember that they were made adjustable, so you could adjust them. Don't be afraid to play with your tension! I've found with my Bernina 230 (which is basically the same as your 240) that I have to tighten the tension when I want to use polyester thread. However, I have my machine tensions set for cotton thread. At the shop where I work, we set the tensions for cotton threads.
Remember that poor quality thread will give you a poor quality stitch. There are lots of great threads out there, just don't buy the 10 for a dollar type threads, and you should be fine.