Unlike with spin rods, you just can't make a cast with a different rod as quickly as you would need to to get a hook up.
..... even if you just put the first rod down without reeling in and tucking everything away, you still need to pick the second rod , strip off the proper amount of line, make a few false casts, and then make your presentation.
That's not just fast enough.....
It's not the same as making a quick cast with a second spin rod.
The reason that the fish blew up on your fly and missed is that bass flies are light weight.
When a bass attacks the bass bug, they're so light weight that they they often get thrown. The bass didn't miss, it pushed the bug away.
Casting the same bug back is the only way to go.
Knowing where the confused bass went to is the hard part.