I bought this butterfly bush from a local nursery about two weeks ago and planted it in a hole double the diameter of the pot and about 1 1/2 times as deep with gravel in the bottom. We have clay soil and not great drainage where I live. I used Miracle Grow potting mix in the hole. Since then we have had lots and lots and lots of rain. I read that these bushes can suffer from root rot if there's not proper drainage, so I dug it up and the roots are not at all mushy so I'm thinking they have not rotted. When I dug it up, there was water standing in the hole. For now, I have put it back in the pot it came in which has lots of drainage holes and set it on my porch under the eaves of the house to shield it from more rain. There is currently water draining from the pot. I have trimmed off the spent/nearly spent blooms. What else can I do to save it?

Let it dry out in the container and when you return it to the soil, just mix plain peat moss in the soil and not miracle grow mix. Peat moss only but mixed with some with the soil will help lower the pH and improve drainage. As a matter as a fact, if you mix peat to your clay soil you will see super results in the garden.

You definitely made the hole twice as wide as the nursery pot which is good. BUT you said that you planted it one and a half times as deep. I hope that the surface of the soil within the pot stayed at the same level once it was in the ground. I hope it wasn't too deep.
By the way, don't put stones in the bottom of the hole. That doesn't do anything to improve drainage!
In clay soil if you plant a bush like this in a big enough hole, they will be just fine. It is what you put BACK in the hole that's important!! Peat moss, topsoil, and maybe a little builders sane would work in a poor drainage area.

No matter what you add to the hole, if the water doesn't drain, the butterfly bush will drown.

Thanks for all the advice. Big Bill I kept the root ball at ground level and backfilled the hole. I was just trying to get the hole deep enough the the roots would have some easy soil to work through before reaching the clay. Sounds like I'll be getting some peat moss And trying again!

Peat moss is added to soil to help it retain moiture.