"I FOUND THE ANSWER!

It’s a hidden detail in the original script.

“MORPHEUS This will feel a little weird.

There are several disturbing noises as he works the needle in.

We MOVE IN as Neo’s shoulders bunch and his face tightens into a grimace until a LOUD CLICK fires and his ears pop like when you equalize them underwater.”

When you enter the Matrix, your ears pop. Scuba divers often can get blood in their ears from this effect. So, the “jacking-in” causes the ears to pop. If repeatedly done (to talk to the machines or to see a woman in a red dress) would mean repeatedly popping your ears—causing them to eventually bleed."