to counter a bomber spam it is best to get tons of fighters. flack are useless against bombers (they do the wrong type of dmg). Your TEC friend has it easier than you, a lvl 3 of the kols flack burst could take out all of the bombers at once if they were in range, leaving him without a fleet. to kill his carriers you should build lots cobalts/skirmishers.

Now for the vasari you probably want a kortul devastator cause it has the Jam weapons ability which can keep the enemy bombers from fireing at you until your fighters deal with them. By the time youve used jam weapons twice or three times the bombers should be almost gone. another suggestion if you are vasari is build 10 or so overseers and micro them so they heal the caps that the bombers are targeting, that way you wont lose your caps as much. 

All good advice. Some additions:

Keep a close eye on that bomber fleet, make sure you know where it is at all times. I think one of the best ways to save your SBs is to engage the bombers before they get to that system. Jump ahead with your fighters and start plucking them out of the sky. Send in your cap ship with antistrikecraft abilities after your fighters have engaged. Also keep your fighters away from the enemy Halcyons, their telekinitic push can level your fighters leaving you defenseless. Set your fighters to attack local are only and keep-em near your fleet if he pulls his bombers back to the carriers. Then move your Caps in close with the fighters supporting so you can get the same anti-strikecraft advantage while damaging your opponents Caps.

In the event you cant get a pre-emptive strike in:

You want to try and keep those carriers in the well with your fighters as long as possible. The longer they are in, the more bombers they will lose. Get your SB up to full health and shields, and upgrade squadron bays to give you some extra bomber killing power. Throw down some repair structures, hangar bays and phase jump inhibitors as they are enticing bomber targets. Build some mines to prevent kiting and most importantly is what Darvin said:

Stay on top of that fleet, strike craft build rate is MUCH slower if an enemy fleet is in the well. With little protection for those bombers, your fighters will be able to kill them seconds after theyre rebuilt and launched. Good luck.