I have never heard of any bad blood between them, but I haven't heard of them being big buddies either. Certainly Bernie has never had a bad word to say publicly about Joe - nor any of the Eagles, actually. He's always maintained that he left of his own accord because the band was going in a direction he didn't agree with, and because the rigors of the road and the fast lifestyle were detrimental to his physical and mental health.
I think Joe was just going for the cheap laugh rather than trying to hurt Bernie, but it was still tacky. JMHO.