Why would Bloodraven not try to attack Bittersteel in Essos, especially when he came into power as Viserys II’s Hand?

Do you mean Aerys I? 

I would think that Bloodraven held back from attacking Bittersteel because a huge portion of the population had just died in a plague, followed by a massive drought and famine.

Westeros was a mess, nowhere near capable of invading the Free Cities, which would have probably brought in Lys, Myr, Pentos, etc. against the Westerosi.