I was reading CFR title-36 327.13 and it says:

(a) The possession of loaded firearms, ammunition, loaded projectile
firing devices, bows and arrows, crossbows, or other weapons is
prohibited unless:
(1) In the possession of a Federal, state or local law enforcement
officer;
(2) Being used for hunting or fishing as permitted under Sec. 327.8,
with devices being unloaded when transported to, from or between hunting
and fishing sites;
(3) Being used at authorized shooting ranges; or
(4) Written permission has been received from the District
Commander.
(b) Possession of explosives or explosive devices of any kind,
including fireworks or other pyrotechnics, is prohibited unless written
permission has been received from the District Commander.

Section 327.8 says:

Sec. 327.8 Hunting, fishing, and trapping.

(a) Hunting is permitted except in areas and during periods where
prohibited by the District Commander.
(b) Trapping is permitted except in areas and during periods where
prohibited by the District Commander.
(c) Fishing is permitted except in swimming areas, on boat ramps or other areas designated by the District Commander.
(d) Additional restrictions pertaining to these activities may be
established by the District Commander.
(e) All applicable Federal, State and local laws regulating these
activities apply on project lands and waters, and shall be regulated by
authorized enforcement officials as prescribed in Sec. 327.26.


So, since bowfishing is fishing, unless the District Commander has actually forbidden fishing in the area, then bowfishing should be okay.

If the District Commander has forbidden fishing or singled out bowfishing, then we need to talk to him.