The 400 and 500 series machines have a drop-in, horizontal plane bobbin. I have done a fair amount of Free Motion Quilting with my 503A, and it often gives me fits with tension; here is what works for me, most of the time:
1. Use the best thread you can find, in a relatively light weight (50 weight, 60 weight ), in both the bobbin and the top thread. Leah Day recommends Aurifil, and it works great with my machine. Polyester better than cotton for this application, in this class of machines; sorry natural fiber purists.
2. Use a Quilting or a Topstitch needle, and bigger than you might otherwise. Replace it often - needles are cheap; what is your leisure time worth to you?
3. Check your bobbin tension using a cheap clip-on postage scale, see The Schoolhouse at the Featherweight Shop for instructions. You want your tension with the bobbin thread you plan to use to be relatively light.
4. Go slow. This can be a problem with the original button type foot controls. I use a replacement electronic foot control, with an external "door stop" so it doesn't run away from me completely when starting.
5. "Floss" your thread through the tension disks to make sure it's really in there, and my machine works better on the outer of the two thread paths through the tension disk stack. Ditch the "tension compensator" on the 500 series, and feed around the center bar before going into the disks.
6. Do not use the current production Singer Brand Class 66 metal bobbins! They are poorly constructed, and the thread catches on the badly pressed in center "hub". I used to curse the plastic Class 66 bobbins because they break if you wind them too fast and hard, but they have smooth, finely finished flanges, as do the METAL bobbins sold by specialists in Singer restoration like Twice Nice in California and Sew-Classic. The original Singer metal bobbins from the 50's are fine, but the new Finest Kind are actually nicer.
7. Clean up any roughness in your needle plate with a teeny diamond sharpener, the one that is a small tapered cone finished with diamonds. Use the Straight Stitch round hole needle plate, and put a piece of tape over the needle position and zig-zag width lever to avoid inadvertent needle strikes when you change sewing modes.
8. I have come to believe that leaving the lifting needle plate down with the stitch length set to zero beats putting the needle plate to the Darning position. Putting the needle plate up changes the relationship with the rotary hook, and I'm not convinced that's a Good Thing.
9. Any of the available Free Motion feet will work, as long as they are specific to Slant Shank Singers. Low Shank and high shank feet will not work, and cannot be modified to work - I've tried. The plastic feet with the arm that rides on the needle bar break eventually. The plastic foot breaks off the plastic and metal jobs with a spring and and arm in time. I haven't used the Big Foot brand, but I just got a Westalee Ruler foot that does not hop, and it works as well as anything else, and it's bombproof. The little spring-steel open toe foot that came with your machine also works, with the presser bar tension set to zero.
10. Pull your bottom thread to the top, every time. See Leah Day videos for a how-to if you need one.
11. Check your tension often, by looking at the back of the work. If it goes to hell, re-thread everything, if that doesn't work, change the needle and re-thread again, if that doesn't work, go to a bigger needle and re-thread again, if that doesn't work, retreat to the Moaning Chair, and weep until the swelling goes away, put your walking foot on, and quilt the project that way. Next week, next month, next project, start over again, and it might work like a dream. The 400 and 500 series are some of the best machines Singer ever made, but they do not excel at Free Motion Quilting. But I have had other machines fight me too...I have decided, for today, to keep my 503A, with all the feet and attachments and bobbins I've accumulated for it, but it's been a near thing lately.