Strafing: If you're at the correct altitude (1-3), one of the buttons for the ASF's firing will highlight ('Strafe'). By clicking this, you can then designate hexes to strafe (1-5 of them, in a straight line, must have flown over them). Once you've done that, you need to select your energy weapons and fire them (only energy weapons with infinite ammo can fire strafe).
Note that the interface will not tell you any of your to-hit numbers, so you'll need to use your own judgement as to whether strafing is worth it (usually it isn't).
Bombing: First make sure the ASF is actually carrying bombs (in the lobby before the game starts right click on the unit -> equipment-> go through the tabs and set up the bomb load). Then, in the firing phase, the different bombing options should be listed as weapons in the weapon list. Again, make sure to be at a correct altitude or it won't work (I'm not 100% on those so I can't list them, sorry).