
DB Basculin sprites.
SV sprites can be found here.
Since you're in an outbreak, save the game once you hit 60 defeated. As others pointed out, shiny basculin is lighter than the original and has slightly yellow tint fins, so as long as your eyesight is decent and the lighting isn't atrocious, basculin is one of those shinies that you think you won't notice but once it pops up it might be rather obvious compared to the others.
As the shiny might take a while to show, I'd recommend you make a sparkling power water sandwich, especially if you're going for multiple basculin. If you aren't sure if you've found the shiny, auto battle the Basculin just to be sure (your Pokemon won't defeat a shiny in an auto battle), and if you accidentally end the outbreak, reset to your last save so you have the 60+ basculin defeated and don't lose your herba. Make sure to save when you know you've found the shiny as basculin carries multiple recoil moves.
If you somehow don't find the shiny and the date rolls over, close out of your game, change the clock back to the date you got the outbreak, and open the game again. I mention this specifically because White Stripe Basculin outbreaks are rather rare and I've personally had to do this.
Hope this helps and you find your shiny!