If you are using NI's PCI-485, then you can setup a system like you described by setting both system's RS-485 ports to 2-Wire Auto. In this mode, the port will only drive transmit when it has data to send. Then your inactive PC watches for activity from the active server (either via the RS-485 port or some other mechanism like a network ping), and takes over when the active server goes down.
By setting the transceivers to Auto mode and making sure the inactive server doesn't transmit unless it knows the active server is dead, you won't double-drive the bus.
Note that 2-Wire auto turns OFF the receiver when transmitting (for 2-Wire communication). Even though you may be using 4-Wire cabling, this could impact your communication. If this is th
e case, you could use 2-Wire DTE w/Echo which uses the DTR modem line (you have to assert/deassert this manually) to control TX Enable, but RX Enable is always asserted.