How do you bypass the heater core on a 1998 Ford Bronco 2?

Disconnect both hoses from the core and one of them also from the engine. Hook the other one back to where you took one off, making a loop. The picture below is not a bronco, but gives you the idea.
By the way, your core is easy to replace. It almost pops right out from under the dash. I ahve included picture below.

Remove and replace heater core procedures:

1. Disconnect the heater hoses from the heater core tubes and plug hoses.
2. In the passenger compartment, remove the five screws attaching the heater core access cover to the plenum assembly and remove the access cover.
3. Pull the heater core rearward and down, removing it from the plenum assembly.

To install:

1. Position the heater core and seal in the plenum assembly.
2. Install the heater core access cover to the plenum assembly and secure with five screws.
3. Install the heater hoses to the heater core tubes at the dash panel in the engine compartment. Do not over-tighten hose clamps.
4. Check the coolant level and add coolant as required. Connect the negative battery cable.
5. Start the engine and check the system for coolant leaks.