Well, first - that list is not that bad. If you trade Bradley straight up - if we want to go down this road - you are probably hoping for a full-season horse, #3/#4 type. That is, not a guy who is any sort of ace, but whose value lies in being able to crank out 30 average-above average starts a season. (basically - Jon Lester) As far as free agency goes - the Sox will take a long hard look at James Shields for sure. He is not a true ace, but definitely high quality and has a history in the division. There are also a lot of other guys (Jorge De La Rosa, Tim Hudson, Ricky Nolasco, Josh Johnson) who have various issues but are very much worth kicking the tires on for Dempster-level money.
For the trade for Bumgarner - he would require more. He is cheap, under control, young, good and the Giants have championship dreams - even if they did not fulfill them this season - and cash. (typical Giants season - if their pitching is good enough to squeeze their putrid offense into October they become very dangerous, otherwise you get a season like this)
If you are going to trade for a pitcher - might as well aim much higher - like King Felix, and for a guy like THAT you start discussing Boegarts.