Is it possible to get research experience between undergrad and grad school?
I spent a year as as a "research student" in Japan doing just that; for me it was between my Master's and Ph.D, but you can also do it after your undergrad.

Basically you need to find a school that offers such positions (here is where I did it), find a faculty member in that school whom you'd be willing to work under, and send them a friendly e-mail to ask whether they can host you.