Here's how Jimmy Rogers sang it. I pieced these lyrics together from several sound samples. It's probably incomplete.

Apparently Rogers recorded it several times, and didn't always use the same lyrics. That leads to some alternative phrasing, indicated by braces {--}.

THAT'S ALL RIGHT

You told me baby, once upon a time,
You said if I would be yours, you would sure be mine,
But that's all right.
{I know you don't love me no more, baby}
{I know you're loving some other man}, but that's all right.
Every now and then I wonder, who's loving you tonight?

...
Yes, baby, that's all right.
Every now and then I wonder, who's loving you tonight?

You told me, baby, your love for me was strong.
When I woke up, little girl, half of this big world was gone,
But that's all right.
{I know you don't love me no more}
{I guess I'll never be the same}, but that's all right.
Every now and then I wonder, who's loving you tonight?