Bodhi wasn't transmitting the plans
That was his initial intention, because the communications tower is theoretically capable of transmitting with the Shield Gate still up:
"To get a signal out, with the shield gate shut? We need to connect to the communications tower; that's the whole point of the thing, to let the Citadel keep talking to the rest of the Empire without opening the defenses"
Rogue One: A Star Wars Story - Official Novelization Chapter 19
Unfortunately, the Death Star plans were too complicated to transmit through the shield gate, as the novelization makes clear:
Even the Citadel's communications tower could not transmit an entire data cartridge with the shield gate in place. But Cassian had already taken measures, through Bodhi Rook, to open the gate.
Rogue One: A Star Wars Story - Official Novelization Chapter 19
"That's a lot of information," Cassian said, "and even the tower won't be able to push it through the shield without data loss. Tell me I'm right about this, Bodhi!"
Bodhi forced himself to concentrate. Audio was one thing, but sending a data cartridge through the shield would be like trying to broadcast it across the galaxy. Too much data, too much interference.
Rogue One: A Star Wars Story - Official Novelization Chapter 20
Instead, Bodhi connected the terminal to the Citadel tower to send an audio message to the Alliance, instructing them to:
- Open the Shield Gate by any means necessary
- Get a ship in position to receive the data transfer
When the console readouts updated to indicate a connection between the ship and the Scarif communications tower, he wanted to weep with joy.
Instead, he hunched over the unit, adjusted his frequencies, and prayed someone would hear him. "Okay, okay," he began. "This is Rogue One calling the rebel fleet!"
[...]
He heard voices in the background—bridge officers, maybe, debating how to respond. Bodhi powered through. "You have to get in position, get ready to receive. And you have to take down the shield gate. It's the only way to get through!"
Rogue One: A Star Wars Story - Official Novelization Chapter 20
Bodhi and his commandeered ship are destroyed soon after this, but by that point it no longer matters; the Alliance have received their instructions.