It would be free with a bank. If you have that much money with the bank, they will bend over backwards for you. For example with E*Trade I think any wire is free if you have 1 million with them.
Or, perhaps more similar to the topic, if I wanted to move a billion dollars from one UBS account to a new UBS account, I certainly could. Some special guy would probably have to turn the key for me, but if I have a billion dollars in a UBS account I surely know that man by name. And also, I would have the benefit of doing it privately, unlike with Bitcoin.
It would require an extra pair of eyes compared to a 1M payment (which are very common), but that's not a significant difference in process, just one more employee would have it in their queue for approval and it wouldn't even increase the time as it'd jump to the front of the queue of payments that need some oversight. It could involve some extra notification as $1B leaving or arriving is meaningful enough to impact your liquidity and reserve requirements and thus your trading desk might need to borrow/lend some cash.
I'd assume that a major bank might have $1B+ payments quite often - I mean, the T-bond market alone is $500B daily and probably some of the individual trades are larger than $1B; then every delivery of a $1B+ industrial project is probably accompanied by a similar bulk payment and the projects across all the industries add up.