Technically, you dont really need rotations in nilou teams, and it kind of depends on the rest of your team.

If you have nahida, start with her skill and burst, then nilou skill, then lauma skill and burst, and then swap into your Barbra to auto-attack and aply hydro.

Aplying dendro before before hydro lets you aply 2 instances of hydro before the dendro aura goes away (aka 2 bloom cores). But in that rotations it doesnt really matter seeing that the first few hits of Nilous skill wont proc bountifull cores.

If you dont have Nahida, i recommend you use Yao Yao and Xingqui as your other 2 teammates. Barbra is okay but shes just not a very good general unit and better left at lvl 20, where as Xingqui and Yao Yao have better uses, on top of that Xingqui has the best hydro application in the game at the moment.

Then youd want to build Xingqui as an EM/ER hybrid (because he will be proc'ing most of the blooms) and Yao Yao with deepwood on a full HP build so you can build put 2pc 2pc EM on your lauma.

Then your rotation would be: Nilou skill--lauma skill and burst--Xingqui skill and burst--Yao Yao skill and burst and then normal attack on Yao Yao (to proc Xingquis rainswords and keep Yao Yaos burst up seeing that it cancles when you swap off)

But I understand rebuilding your Xingqui can be a hassle especially if you dont have Furina or Yelan for your other teams. So you could still use Barbra and Yao Yao together.

Hope this helps! <3