sticky rubber?

[i-want-that-tee.livejournal.com]

Hello ladies, I found a wonderful 50s-bag while thrifting, it's made of some rubber-y material mocking ostrich.

After I cleaned it (it was quite sticky and dusty), the stickyness did not disappear and it doesn't feel nice at all...

Has anyone suggestions how i could get rid of that? 
I just used regular soap and water.
Thanks in advance, I'd honestly love to wear it and I'll definitely post pictures, as soon as I can touch it without going "ewwwwww" ;)

edit: Thanks so much! I know what I'll be doing the next few days ;)