If you tighten the bobbin tension a tiny bit at a time, you should eventually find the setting at which the problem goes away.
When the stitch is balanced, the bobbin thread doesn't show on the top and the needle thread doesn't show on the back. You can even use vastly dissimilar threads in the needle and bobbin as long as you get the tensions balanced.
Don't be afraid to adjust the bobbin tension for the thread that you're using in the bobbin. It's easy - and it's more fun to sew when you're using the materials best suited to the final result that you're looking for. :)