bombers dont work because i had to switch all my strikecraft slots to fighters just to hold off his own strikecraft
Fighters are actually not all that good against fighters...flak is far far better, and capital ship abilities (flak burst, magnetize, TK pusch, Jam weapons) are very handy...I have a distorted intuition on this since I play with a mod, but fighters in general don't suppress bombers very well, especially when there are lots and lots of bombers...
If you are TEC, ogrovs + bombers are a good way to deal with starbases...wiping out support structures first (repair bays, hangars) should be your first priority...having an akkan with targetting uplink is also very useful...garda's should be fine for dealing with enemy fighters...
If you are Advent or Vasari, then lots and lots of bombers...
If this is an AI starbase, then honestly a full fleet could probably just shred the TEC starbase...once your bombers have been whittled down by enemy fighters, just throw in tons of LRMs and/or Kodiaks....if it is a human starbase, be careful as it likely has the red button on it....