I had this exact problem with the Bose system in my this weekend Armada. Basically the output from your Bose head unit is "line" or low level, and the output of the Avic is "speaker" or high level.
The solution was very easy (which I got from Crutchfield). I could have used my existing PAC line level converter (and have yet something else to squeeze behind the dash), but instead just soldered on RCA connectors.
On your aftermarket harness (that plugs into your factory harness) you have 8 wires for the speakers (white, gray, green, voilet; then 4 more with a black stripe).
The solid colors are positive, the black stripe are negative.
1) Take an old RCA cable with male plugs on both ends (ie: patch cable).
2) Cut it in 1/2.
3) Strip the outside jacket.
4) You will have an outer stranded wire (positive) and an inner sheilded wire (negative). Similar to a COAX cable.
5) Take one RCA plug per two speaker wires of the same color.
6) Take the negative (color with black stripe) and solder it to the inner core wire.
7) Take the positive (solid color) and solder it to the stranded wires.
Make sure you insulate (ie: separate) them from each other (I used heat shrink on each connection, then one over the whole thing.
9) Repeat for other three wires.
Now your harness will have the 4 RCAs coming out if it. Plug these into the corresponding female outputs on the Avic harness for front and rear.
You will not believe how good it sounds! I hate Bose and everything they stand for but my Avic sounds so nice I'm tempted not to install aftermarket speakers. 
The highest volume of the Avic is just on the cusp of distortion so you have a nice range to play with.
Note: The F90BT has 4 volt pre amp outputs which is enough to feed the Bose amp. If they were 2 volt the volume might not be high enough and I might go with the line level converter.