Looks to me like it is on felt. I would hoop my stabilizer, lay a piece of felt on top of it and go around with the first color. Take the hoop off the machine (DO NOT take the stabilizer and felt out of the hoop.) and carefully!!!cut around the outside of the line. Put your hoop back on and you may want to back the thread sequence back to the first color then continue as usual. it is a very pretty bookmrk--good luck.
What type of stabilizer. I tried it with tear away and around the bookmark it looks fuzzy. But I also dont like the back, so next time I am going to put somethin as a backing befor last stitch. How do you back your thread sequence?