Hi Chris,
My bus is built exactly like this one: http://datasheets.maximintegrated.co...80-MAX3089.pdf (page 20)
Yes and no..... The actual bus may be built the same but your tranceiver chips (the MAX3081) doesn't have the DE-pin which you see in the schematic on that page and which you need for multidrop networks so yes, the MAX3081 is basically intended for point-to-point.

If the tranceiver has no way to turn of its driver then it will always drive the bus to one state or the other. Then, when another tranceivers driver is hooked across the same pair of wires and IT too tries to drive the bus to one state or the other there will be a conflict. One tries to drive it high while the other tries to drive it low - for example. On the chips with the DE-pin (Driver Enabled) you can disable the driver outputs all together.

/Henrik.