What is a good bomber to fighter ratio?

Truthfully, I find that carriers are too costly for the amount of firepower you get. The same resources spent on LRMs or heavy cruisers usually yields better results.

That said, if you're going to use strikecraft, the fighter to bomber ratio you choose will be dependent on what kinds of forces your enemy is fielding. If he's going in for LRM spam, I'd have the majority of my strikecraft squadrons be fighters, since fighters are good against LRMs. If your opponent is anchoring his fleet with something other than LRMs, then you have more leeway. In the abscence of LRM spam, your ratio will be dependent on how many fighters he has. If he has a lot of fighters, I'd split 50/50 fighters and bombers. If he only has a small force of fighters, I'd go 1/3 fighters and 2/3 bombers. Also, if he has a lot of flaks, I'd bias more towards bombers since they are more surviveable against flak.

I'm a newb at this - just AI only so far, but fighter survivability is a bit low for my tastes. I don't use hangars anymore - I find my tactical slots and resources are better used elsewhere - mostly ships, repairers, jump inhibitors and a few turrets if I have the slots to spare. By late game, culture dissemination is rather nice. On my cap ships I go with 100% bombers for good damage and survivability and use flak frigates for dealing with strikecraft. I'd rather have flak frigates over fighter squadrons anyday.

My standard fleets have a battleship, carrier, buffer cruisers, lrms and flak - eg for Advent, Radiance, Mothership, Guardians, Illuminators and Defense Craft. I keep one fleet guarding each choke point with my empire safely behind. Even without caps, it's amazing what a few Guardians, Illuminators and Defense craft can not only hold off, but completely destroy with the aid of a few repairers and a jump inhibitor.

I go 50/50 for my carrier units in fleets, but a 2 to 1 ratio of fighters to bombers in my planetary hangar defenses.

The main advantage of strike craft over other types of units is speed, not firepower. Strike craft can cross the gravity well to hit targets that are trying to avoid your fleet, they can chase down fast frigates and scouts, and keep putting the hurt on your enemies regardless of how they maneuver. Yes, flak counters them very effectively, but you can focus fire flak pretty easily with the rest of your fleet.

I'd advise staying away from carriers. However, hangar defense honestly isn't too bad. The thing with hangar defense is that you still need to scout to know what strikecraft to build. Remember that you can scuttle strikecraft, allowing you to build some of the other type.

In general, people attack with fleets consisting of mainly HC's or LRM's as their DPS. Against lrms, have fighters. Against HC's, have bombers. Keep scouts out to know what your enemy is attacking you with. If they bring in carriers, then obviously use fighters. However, carriers aren't as much of a threat as HC's or LRM's

Also, keep in mind that flak counters fighters very well, but isn't as effective against bombers. Furthermore, bombers have more HP. Because of that, if they come in with lots of flak and bombers, it may be worthwhile to keep most of your strikecraft as bombers with a couple on fighters to fight the ones that their cap ship sends out.