Oh my, how coincidental!
I just finished (I lied, not finished... but practically finished!!) making a bear-backpack!
That bunny is adorable, though personally I would prefer if the ears were flopping down. Anyway, I made a pouch. And I free-form cut shapes for the pouch without thinking about it too much (that bit me in the butt later). Two half-circles and two triangles. I'll MS-Paint a picture.

(Um, switch the position of the half-circles. The flat edge is where you gather, the round is where you sew.)
Yeah, so, something like that. I made it out of a stretch velvet (I think that's what it is, that cheap stuff the stores put out for Halloween that they call velvet, but it's not real velvet which the stores call "Royal Velvet" and sell for a good 20+ a yard...) so it would stretch to accommodate anything I shoved in there. I basted the top and gathered it so it would fit the hole in the bear. To close it, I was planning on putting a zipper in, but I've never done it and I didn't want anyone to have to help me so I parted the fur a pierced eyelets in it. I threaded two different ribbons, a hot pink slender one and an embellished cream one and that will close it. I just have to, you know, not put anything too big in there so I'll be able to get it out without unlacing the whole thing.
Anyway, as for the straps, I bought... oh, what's it called? Trims? I bought, from the various trimmings isle, pleather eyelet cord/ribbon/finishing/trim/fabricstuffs. I also bought a four-pack of small D-rings and two small parachute clips. I cut enough of the pleather for around one-and-a-half of my height (which seemed like a lot but I only had a few inches left when I was done). I sewed a D-ring to the top and bottom of the opening on the bear, then... Oh, another picture. -MS painting-

I secured the straps from slipping out by sewing through them with the narrow, hot pink lace. (Btw, the colour of my bear is white with hot pink flecks in the fur. I know I have no sense of colour-coordination.) I also sewed the D-rings on with both different laces. You should be able to fit two straps per ring, in case you didn't know, and if it doesn't fit then make it.
Anyway, I ended up making wrist+ankle+neck ruffles for it. Well, at least, I
had a wrist ruffle and
an ankle ruffle, but the ankle ruffle fell off at Six Flags and I will make the neck ruffle with the cutest little heart-shaped Lolita key ever on it! Yup. Also, note that I ran out of lace because the ruffles took up HELLA LOTS of lace. Like, at least 30in minimum became a 6-inch ruffle. Yup.
...
Oh, you're making a purse. Right. Well, then you only need one strap. Lucky you! Less work! 'Cos getting that thicker cream lace through that ******** thing was like... erglesnarf. So. Have fun.
Tell me how it comes out, ne?