I have almost completed a sample to demo how to geocode / reverse geocode using Bing that I will release shortly. If its helpful I can also make a sample to hit ArcGIS Server.
Basically how to structure your calls and then create a point on the map with the result from the server. We've written many samples in other ESRI products to do this, but one specifically for ArcGIS Explorer I am sure would be helpful.
This is your intended work flow correct, call from your firetruck to your fire dispatch web service to geocode you?
If the above is correct, there are two ways to achieve this without having to write any code at all. You can repoint ArcGIS Explorer to use your own geocoding, placefinder or routing services. Open the Application configuration manager and click on the Custom Resources tab, at the bottom you will see Choose Services..., simply add your services here. Then the directions control, routing and find controls will use your geocoding / routing services. Otherwise you could use the exisiting services we provide. In either case if you combine with the GPS add-in I have on the labs site you will have your current location which should solve your issue. You will see your location, if you then capture your location as a point note (part of the add-in functionality) you can then drag and drop that note into the directions control. I assume you would have the destination already. Then all you have to do is query for a route.
I am actively working on the GPS code in support of SAR teams. The add-in now supports (not released) the Infinity radio and GPS mic. Connecting one of these radios will not only give you your own location, but the locations of any other radio broadcasting their location. They are brilliant radios, as not only can you use them as a normal TX and RX radio, but you get all of the locational data also, including comments etc.
Next month is a SAR meeting being held in Yosemite, I will be there demoing this add-in with the Infinity radio code added and a few other possibly interesting add-ins. Also participating will be Tom Patterson, ESRI's Wildland Fire Specialist, Tom has a wealth of knowledge in this field.
I hope that this helps,