TanCalGal If you spray with Raid and wait a day and then, wash with soap and water, it should remove the bugs. But I do not think you will ever be 100% sure there are no bugs, the bugs can hide deep in the wood for a long time. Some say to shellac the branch and that might work, but still not a 100% guarantee. You can hang with velcro. As an alternative you can stencil a branch to the wall or hand draw a branch lightly in chalk and fill in with paint. Here's a stencil from StenSource. This stencil would look more like the tree branch you like, if you didn't stencil the leaves, and only stenciled parts of the tree branch http://www.stensource.com/#catalog.php%26prodid%3DBD7002%26resultpage%3D1%26index%3Dproduct%26RPP%3D20
Here's the link to the fabric:
http://www.amazon.com/gp/product/B0042TSDAE/ref=s9_wish_co_d45_g201_ir01?ie=UTF8&colid=R49WO7Q65EEX&coliid=I2PJ2GD32F5TRN&pf_rd_m=ATVPDKIKX0DER&pf_rd_s=left-1&pf_rd_r=13HFS3XZDS2VQ8VFXQJR&pf_rd_t=3201&pf_rd_p=1280661682&pf_rd_i=typ01