Bribery is usually illegal, but it has some specific requirements. The giving of gifts in not illegal, if that is all there is to it. It's the quid pro quo that is tough to prove, and illegal. I figure in any political kind of case before SCOTUS, the votes are pretty much a foregone conclusion for most of them. They don't need bribing.
Now, if you could point to an unexpected ruling by Thomas that clearly benefitted said billionaire ...you could have a basis for impeachment, and then trial.
We don't impeach Congressmen, it was done once, sort of, long ago.