No, don't need bidirectional lines, but do need data to go both directions.
So make a board with 3 connectors:
AVR Programmer:
Reset
+5
Gnd
SCK
MOSI
MISO
1.8V Board:
1.8V
GND
1.8V Reset
1.8V SCK
1.8V MISO
1.8V MOSI
1.8V Tx
1.8V Rx
FTDI Basic:
Tx
Rx
DTR
Gnd