Man, I hate to bring this up. But, because bowfin don't occur naturally west of the Rockies, they're illegal in CA, OR, and WA due to the probability of bowfin being detrimental to pacific coastal habitats, waterways, and species. Read 'em and weep:
CALIFORNIA prohibited fish species -- illegal to import, transport, or possess live specimens w/o a permit
(4) Class Agnatha - Jawless Fishes
(A) Family Petromyzontidae - Lampreys All nonnative species (D).
(5) Class Osteichthyes - Bony Fishes
(A) Family Percichthyidae - Temperate Basses
1. The species Morone americana (White perch) (D).
2. The species Morone chrysops (White bass) (D).
(B ) Family Clupeidae - Herrings Dorosoma cepedianum (Gizzard shad) (D).
(C ) Family Sciaenidae - Drums Aplodinotus grunniens (freshwater drum) (D).
(D) Family Characidae - Characins
1. Astyanax fasciatus (Banded tetra) (D).
2. All species of the genera Serrasalmus, Serrasalmo, Pygocentrus, Taddyella, Rooseveltiella, and Pygopristis (Piranhas) (D).
3. Hoplias malabaricus (Tiger fish) (D).
(E) Family Salmonidae - Trouts Salmo salar (Atlantic salmon) - Restricted in the Smith River watershed (D).
(F) Family Lepisosteidae - Gars All species (D).
(G) Family Amiidae - Bowfins All species (D).
(H) Family Poeciliidae - Livebearers Belonesox belizanus (Pike killifish) (D).
(I) Family Channidae - Snakeheads All species (D).
(J) Family Cyprinidae - Carps and Minnows
1. Leuciscus idus (ide) (D).
2. Ctenopharyngodon idellus (Grass carp) (D), except that permits may be issued to a person, organization or agency for possession of triploid grass carp, under conditions set forth in Section 238.6.
3. Hypophthalmichthys molitrix (Silver carp) (D).
4. Aristichthys nobilis (Bighead carp) (D).
(K) Family Trichomycteridae (Pygidiidae) - Parasitic Catfishes. All species (D).
(L) Family Cetopsidae - Whalelike Catfishes. All species (D).
(M) Family Clariidae - Labyrinth Catfishes All species of the genera Clarias, Dinotopterus, and Heterobranchus (D).
(N) Family Heteropneustidae (Saccobranchidae) - Airsac Catfishes All species (D).
(O) Family Cichlidae - Cichlids
1. Tilapia sparrmani (Banded Tilapia) (D).
2. Tilapia zilli (Redbelly tilapia) (D), except permits may be issued to a person or agency for importation, transportation, or possession in the counties of San Bernardino, Los Angeles, Orange, Riverside, San Diego, and Imperial.
3. Tilapia aurea (Blue tilapia) (D).
4. Tilapia nilotica (Nile tilapia) (D).
(P) Family Anguillidae - Freshwater Eels. All species of genus Anguilla (D).
(Q) Family Esocidae - Pikes all species (D).
(R ) Family Percidae - Perches
1. Perca flavescens (Yellow perch) (D).
2. Stizostedion vitreum (Walleye) (D).
(S) Family Catostomidae - Suckers All members of the genus Ictiobus (Buffalos) (D).
(T) Family Cyprinodontidae - Killifishes Cyprinodon variegatus (Sheepshead minnow) (D).
(6) Class Elasmobranchiomorphi - Cartilaginous Fishes
(A) Family Carcharhinidae - Requiem Sharks All species of genus Carcharhinus (Freshwater sharks) (D).
(B ) Family Potamotrygonidae - River stingrays All species (D).
Source: California Code of Regulations, title 14, section 671. These regulations are promulgated by the California Fish and Game Commission pursuant to statutory authority set forth in the California Fish and Game Code. (There's a statutory list too, but the one from the regulations is more complete. The statutes only contain the original list, whereas the regulations also include all species added by the Commission.)
OREGON -- Live specimens of the following fish species may not be imported, possessed, sold, purchased, exhanged, or transported in the state:
(A) Order Amiiformes
Bowfin - Amiidae - Amia calva.
(B ) Order Cypriniformes
(i) Piranha or Caribe - Characidae subfamily Serrasalminae - All species and hybrids except Serrasalmus, Pygocentrus and Pristobrycon pursuant to ORS 498.242 and OAR 635-011-0160(2);
(ii) Walking catfish (ORS 498.242) - Clariidae - All species and hybrids;
(iii) Oriental weatherfish - Cobitidae - Misgurnus anguillicaudatus;
(iv) Ide - Cyprinidae - Leuciscus idus;
(v) Rudd - Cyprinidae - Scardinius erythropthalmus.
(C ) Order Lepisosteiformes
Gar - Lepisosteidae - All species and hybrids.
(D) Order Perciformes
(i) Snakehead - Channidae - Channa All species and hybrids;
(ii) Round Goby - Gobiidae - Neogobius melanostemus;
(iii) Ruffe - Percidae - Gymnocephalus cernuus;
(iv) Zander or Pike-perch - Percidae - Stizostedion lucioperca.
(E) Order Salmoniformes
Pikes, Pickerel - Esocidae - All species and hybrids.
Source: Oregon Department of Fish and Wildlife regulations, Oregon Administrative Rules (OAR) 635-056-0050 (Prohibited Species), subd. c.
Restricted Fishes of Washington
(i) Family Amiidae: Bowfin, grinnel, or mudfish, Amia calva.
(ii) Family Channidae: China fish, snakeheads: All members of the genus Channa.
(iii) Family Characidae: Piranha: All members of the genera Pygocentrus, Rooseveltia, and Serrasalmus.
(iv) Family Clariidae: Walking catfish: All members of the family.
(v) Family Cyprinidae:
a- Fathead minnow, Pimephales promelas.
b- Grass carp (in the diploid form), Ctenopharyngodon idella.
c- Ide, silver orfe or golden orfe, Leuciscus idus.
d- Rudd, Scardinius erythropthalmus.
(vi) Family Gobiidae: Round goby, Neogobius melanostomus.
(viii) Family Lepiosteidae: Gar-pikes: All members of the family.