with my bitcoin floating around somewhere.
The Blockchain is the definitive record of where that money is. Once there are about six confirmations there is no reasonable doubt about who now has control over that money
Bitcoins don’t really float about anywhere indeterminate. They are either under your control or under the recipient’s control.
I believe there is the possibility of a fork in the blockchain and for the network to converge on a fork that has your transaction in a slightly later block than your wallet initially indicated – but that’s relatively rare and I suspect wouldn’t make any difference after an hour or so in most cases.
Is there a way to recover the bitcoin.
After six or so confirmations, the only feasible way is to ask the recipient if they are willing to return the money to you.