In some Sci=fi shows/films, certain bombs/mines have the ability, once deployed to MOVE towards targets.. How would something like that work for a X-wing game? What cost increase would this be for regular bombs, or would they not be something that could get 'upgraded', just used on new bomb types??

Isn't that just a low velocity (relative to the target) missile or bomb equipped drone?

it's already somewhat represented in the game. just stick dead mans switch on a ship and fly in, use the autopilot drone, use buzz droids as they are or design your own remotes. launching devices and dropping them with different templates is not technically moving them toward a target, but it can have a similar effect. i'm thinking emon azzamen or sol sixxa with skilled bombardier. if you want to use house rules, just use the rules for drk-1 probe droids, except make which ever ship is overlapped by the remote roll a couple of dice and take what ever damage is on the dice.

Meffo hit all the relevant points. The rules for relocating remotes gives a framework for "homing mines" to move around after being placed, so it's possible to introduce them.

I'd imagine we will see them in the future. Could be as a mine or a remote. Would either need to be low damage or high cost as it would require less skill to hit. Sabine would be even more powerful.