Are there any restrictions/codes that would prevent a soffit vent
from being installed outside the bathroom window? Since I don't
open the top half of the double hung window there is almost no
possibility of the exhaust re-entering the house through the window.

Some areas, Dallas for instance, prohibit soffit openings within four
feet of windows or doors. In case of a fire, this keeps flames from
going directly into the attic. I hear that California prohibits soffit
openings completely, at least in some areas, because of brush fires. I
hear they allow them with special self-closing louvers.

Check with the code office.

--
Steve Bell
New Life Home Improvement
Arlington, TX USA