Let's see, I'm no expert but will take a shot an answering.

After you install your new servo, all of the centering and direction of operation is controlled from your radio transmitter. Changing one servo in a group of three, might cause you to need to re-check your swash-plate in mid and full stroke. See video link below. Making sure your swash-plate is level will make your heli hover and fly better/easier.

The mixing is done in your radio transmitter. That's were all the smarts are. For a Collective Pitch (CP) heli like your Honey Bee King, the mixing in the transmitter is called CCPM (Collective Cyclic Pitch Mixing). Causes all three servos to move together to raise your swash-plate (moving blade pitch) along with your throttle. And your cyclic control still works to tilt the swash-plate at the same time if you tell it to ... pretty smart.

Here are some useful videos for setup that might help you. Be sure to watch the CCPM setup parts.

http://www.helifreak.com/showthread.php?t=41692

Let us know how this turns out?