According to the wiki serpents only spawn in full ocean biome at night or in storms. Also their spawner has a 1000s cooldown so you shouldn't recheck any particular spot more than once every 17 minutes.

https://valheim.fandom.com/wiki/Serpent

I'd take a longship and just cruise around exploring. Try to stay with the wind so you can cover more ground, use moder power if you got it.