I had just the same experience. It was only one occasion but I did nothing more to the site then putting it under a new account on my shared hosting, so only the last digit of the ip has changed. I saw a drop in rankings however the original I gained back the original rankings a few weeks later.

Egol has usually got great answers that woths linstening to, this time however I think I disagree as moving site A's hosting to a new ip causes a drop in rankings. Put the redirection on top of that and you get some more fallback. I think in the above case I would not change the hosting but do the redirect and wait for google to notice the change. Maybe a few months later I would give up site A's original hosting and migrate it to site B's hosting to be able to keep the original urls live for some more time.