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Vasari are constantly on the offensive, if you aren't building a starbase in every system as part of your assault doctrine you are doing it wrong.
Starbases are extremely expensive investments. It's often a good idea to invest primarily in Assailants/flak/bombers instead, because they can be used in more than one gravity well while having a large amount of damage output.
Also, the Vasari are actually best on defense, although they do have powerful offensive abilities. However, think of Phase Jump Inhibitors, Gravity Bomb, very strong moving starbases, Phasic Trap, Overseers, Subverters...very often when I'm playing Vasari I try to lure my enemy into jumping into my system with an Orky and a couple PJIs, allowing me to destroy their entire fleet.
Then again, I play competitive PvP instead of against the AI, and you sound like you're playing against the AI.
You don't need strong ships because 40 bombers will just annihilate everything in their path. Get a carrier as your first cap with the fleet heal ability and nothing will ever die.
Having a good number of Assailants will help a lot as well, especially given that the AI will always spam tons of light frigates early in the game.
If you want to discuss this more, make a new thread.