Don't toss good bait! Send it to me, I'll always find time to use it.You only need to keep 4 baits on hand (Crawlers, Guts, Worms and Insect Parts) toss the other baits you get. Note, if you get bait at a fishing hole, that bait will be used somewhere else, not where you are.
If you want to be a provisioner - YES.
If you want dyes, acheivements and quick gold - YES
If you want to play CoD - NO.
A quick tip for anyone starting out:
Ocean baits are worms (Found as loot from undead enemies and can be found when harvesting plants) and chub (Found by fishing in foul water)
River baits are Insect parts (found from harvesting flying insects) and Shad (found by fishing in Lakes)
Foul Water baits are crawlers (found by killing and then looting level 1 land insects, such as centipedes or level 1 spiders) and Fish Roe (found by fishing in rivers)
Lake baits are Guts (found by killing and then looting small livestock - from rates to sheep) and minnow (found by fishing in oceans)