Keep your bombers docked at first and draw his fighters into your flak. Then spam away. Or build your own starbase (With the construction being defended of course.) there and attack with that.

Or just ignore it and go around it.

As Kitkun said, avoidance.  Scout wells first, never jump in blind.  That way positioning wont matter, he can't guard both ends of a phase lane on most planets, it has a 12km range.

Should you end up in a situation where he actually can guard both ends of a phase lane, low gravity roids are about a hairs difference from optimal positioning, move through in shifts just far enough apart for the preceeding group to get out of range.  You can only blow a starbase up once.

It also has a three second delay, something the Vasari are uniquely qualified to exploit.  You have a certain capital ship that can take itself out of phase, tag yourself as soon as you see the explosion start and you have a ship guaranteed to be able to bypass the station.  With the phase gate ability, you can move in from the next planet and strike from the other side of the well.

This isn't a rule of thumb, this is just a rule:

Always presume a TEC player with more than 5 military labs has rigged all his starbases to explode

If you do not make this presumption, you will eventually (and in your case, frequently) lose your fleet.  It's not fun when this happens, so always presume that you're walking into a death-trap.  You do have some good options, though, especially since you're Vasari.

Look before you leap.  Send a scout first to identify where the starbase is, then jump your fleet in somewhere else.  Doesn't matter what faction you are or what faction you're against or what stage of the game you're in, this is just a good idea so you always jump in at the most favourable angles.  If you don't have scouts, flak frigates make a good alternate due to being very tough and relatively inexpensive, but do try to bring along some scouts (they're not terible combat units, either.  Set them to auto-attack and they'll contribute reasonably well in the fleet battle).

So, let's move on to some tactics.  Kitkun has already explained the obvious one of docking your bombers rather than letting them get whittled away.  However, a smart opponent will simply counter by doing the same thing, docking his fighters (or setting them to local targeting) rather than allowing them to engage your fleet and get killed. 

If you want to keep using bombers, you just need to compensate with numbers.  Bring an inordinate mass of bombers so you can kill the starbase before they get whittled away.  Somewhere in the range of 70-120 squads should be sufficient if you have maxed out your phase missile upgrade (this is under a third of your maximum fleet command; I routinely pack carrier forces this large to bring down problem starbases in the end-game).  You seem to be late enough in the game that this is very viable.  If he doesn't have Kols nearby, your best option is actually to set the bombers to "hold ground" behavior and order them to move right next to the starbase.  They will cluster up very tightly, and this makes them difficult for flaks and fighters to attack (but very vulnerable to a Kol's flak burst, so don't do it if you see a Kol).  It should be noted that the counter to this for the opponent (barring a high-level Kol) is setting his fighters to hold ground behavior and setting them right next to your bombers.

Now, let's move on to tactics that involve using frigates.  The "boom-base" has one glaring tactical fault - it affects friendly as well as enemy units.  This means that any defenders next to the starbase when it blows will also be destroyed.  This limits the ability of an enemy to keep his units next to the starbase and defend it appropriately.  One of the best ways to capitalize on this is to send in a smaller strike force (rather than your whole fleet) into range.  Even if he explodes, he's only destroying maybe 40-60 frigates (fewer if he didn't invest many upgrades in the starbase), and the rest of your fleet can swoop in for the kill.  Make sure to knock out repair platforms and hoshikos first; these can cause the starbase to repair up to 70 hit points per second, and a small force won't be able to overwhelm that much healing on top of the starbase's superior mitigation and armor. 

Another great option is the Vasari superweapon, the Kostura.  This weapon will stun all units and structures in the target gravity well (in the upcoming patch, which is currently in beta testing, the Kostura no longer affects units, only buildings).  If you have two of them, you can stagger the shots to keep the starbase stunned.  If it doesn't have enough hull upgrades, you can kill it before it recovers.  This is risky, because it only takes a moment to activate once it recovers, however this would work quite well combined with a small-medium frigate-force I described earlier.

Happy hunting!

I was wondering when that was coming....