Yes, all bugs and fish are limited during the time of the year AND time of day. If you check your encyclopedia, it'll highlight the months in which that bug or fish is active as well as during what time of the day. You can find sites on guides for the fish and bugs needed for the time of year, etc. This is important to know as bugs and fish become inactive during some months, so they're not able to be caught at all no matter how hard you look. Here's an example for May in the nothern hemisphere:
Critter type Critter Location Shadow size Time
Bug Great Purple Emperor Flying N/A 4 a.m. - 7 p.m.
Bug Queen Alexandra's Birdwing Flying N/A 8 a.m. - 4 p.m.
Bug Banded Dragonfly Flying N/A 8 a.m. - 5 p.m.
Bug Pondskater Ponds N/A 8 a.m. - 7 p.m.
Bug Diving Beetle Ponds and rivers N/A 8 a.m. - 7 p.m.
Bug Violin Beetle On tree stumps N/A All day
Bug Rosalia Batesi Beetle On tree stumps N/A All day
Bug Scorpion On ground N/A 7 p.m. - 4 a.m.
Fish Frog Pond Small All day
Fish Catfish Pond Large 4 p.m. - 9 a.m.
Fish Nibble Fish River Smallest 9 a.m. - 4 p.m.
Fish Angelfish River Small 4 p.m. - 9 a.m.
Fish Betta River Small 9 a.m. - 4 p.m.
Fish Rainbowfish River Smallest 9 a.m. - 4 p.m.
Fish Giant Trevally Pier Large All day
Fish Mahi-mahi Pier Large All day