Michelle, it took a while to get back to you (don't have to clean house when you quilt but you do have to go shop for food...
). I went ahead and did another stitchout of my invisible applique stitches because I wanted to see how invisible I could get them and then tell you what I had done.
So, on my Bernina 830, I used the invisible applique stitch #1331, stitch length .8, stitch width.9, tension .05 (although tension will vary depending on fabric, thread, etc.). My understanding (I called my friend at the Bernina dealership) is that the stitch on your Bernina 153 that is roughly equivalent to mine is called the vari-lock stitch and should be among the top ten stitches displayed on your machine.
I used a size 70 universal needle to do this and believe this gives the smallest hole. I think you could probably use a size 60 or 65 needle too. If you notice from the picture below, you can see a teeny bit of my Aurifil 2370 coming up into the YLI invisible thread, but my understanding is that this will disappear with the first wash. Yes, if I take my bifocals off and put my nose right up to the block, I can see the tiny bobbin stitches but you otherwise don't really see them. Since I made my circles exactly like you did (with the exception of having used double freezer paper to make the circle), I think they will puff up and you will see neither the top bite nor the tiny stitches from the bobbin (they will get covered up by the puffy circle. Since you probably are using various colors on the background where your circles are lying, I would choose a medium thread that blends among the background colors you are using. And if all else fails, Aurifil #2370 always seems to do the trick.
Let me know how it works out for you and if there is anyone else who would like to pipe up about the topic, please! I've never done invisible applique before so this may just have been a lucky day for me.