Flaks can fire at bombers but are not very effective against them; their weapons are anti-[very light] so only do 75% of their base damage versus bombers, which have light armour. They are more effective against fighters, which have very light armour, and do 133% base damage.

The best counter is fleets of fighters, which do anti-light damage (200% of base damage). You can also use corvettes, which have two banks (left and right) of anti-light weapons that can fire at strikecraft. If you can deplete the antimatter of the carriers and keep it depleted, this will stop the bombers coming back since they can't be manufactured (particularly so against Vasari bombers which need 50 antimatter per bomber).

Flak Burst (Kol) and Telekinetic Push (Halcyon) can be used if you've got the cap ships but have a limited range and cost a lot of AM. Jam Weapons (Kortul) is effective if you've got the fighters or corvettes to clear the bombers up (or you're just delaying the inevitable). All three need good micromanagement (so turn off the AutoCast) to get the most out of them and you need to make sure the bombers don't kill said capital ships too quickly. Vengeance (Rapture) at high levels is highly effective if the bombers are focus-firing a target, you know which ship they are going for and you can cast it on that target before your opponent figures out what you are going to do.

If you're up against the AI, then you could always try luring the fleet into a grav well that grounds strikecraft (e.g. plasma storm) or you can cause bombers to suicide each other if they are in tight groups at a gas giant planet (although be aware, the explosions affect everything, so you need to intercept the bombers with fighters or corvettes before they reach your main fleet).

As pointed out, fighters are the main counter to bombers.  It is also worth noting that basic light frigates will shred carrier cruisers.  This won't help you out much if the carriers are well defended by a starbase, titan, or a reasonable sized fleet, but if the carriers go on offense with no support, you can kill them pretty quickly with massed light frigates, though you will take some bomber damage in the process.

You could try scuttling (thin stripy yellow and black button below picture window in the centre) your flaks and replacing them with carriers. Particularly with a titan, you don't want to be giving it free XP, and scuttling ships with 100% hull gives you back 30% of the resources. AFAIK there is no mass scuttle button (which is annoying), so you have to scuttle each ship individually.

As TEC, EMP Bomb is excellent for depleting antimatter, which should in conjunction with Disruption Matrix, slow bomber production against the AI (the AI stupidly brings its carriers close to the main fleet so you should be able to get them easily). Magnetize may also help once the bombers are mostly destroyed.

Remember to keep your carriers away from the titan and the accompanying fleet.