Music in your podcast is a very touchy subject. One that you shouldn't take lightly. There seems to be a new algorithm that recently released that is again bringing music licenses to the forefront of the conversation. Podcast hosts such as Libsyn and Blubrry have recently said that in a single day they have received more takedown requests than they had in the past decade. According to Rob Walch at Libsyn "there is no legal license that allows podcasters to use copyrighted music" Companies might sell you one but they do not include "mechanical" transfer of content. This means you are recording the copyrighted material for play at any time in the future, with no limits on how often. It is a complicated mess and there are much better out there to explain this, as we are not lawyers and just repeat what we hear.
The good news Buzzsprout has just published an article on Podsafe music and where to find it. Still, be sure to read all the fine print in the sites they recommend and follow it to the letter.