Does the Blunderbuss require you to use only the +2 strength bonus in order to use its roll effect?
If you choose to gain the bonus, then you must add 1 success for any 6 rolled (after the rerolls, if applicable) and substract 1 success for any 1 rolled (after the rerolls, if applicable).

But the bonus itself isn't special. As always, you apply the highest available bonus. If it's not the bonus provided by the Blunderbuss, that doesn't affect the other ability in any way.

The choice to gain the bonus activates the other ability, not the fact of applying the bonus.

The card could be as well written like this:


  When resolving a Combat Encounter, you may gain +2 Strength. If you do gain the bonus, each 6 you roll when resolving a etc etc


Edit:
I have asked Nikki Valens - Eldritch Horror's designer, for an answer.

Here it is, with emphasis added in the most relevant part:


  The blunderbuss has a potencial negative effect in that rolling 1’s will negate successes. It may be that an investigator does not wish to use this effect. For this reason, the bonus and the other effect are tied to an option on the investigator’s part. The investigator may choose to both gain the bonus and the other effects (6’s are two success and 1’s negates successes). Even if the investigator applies a higher bonus from another effect, the 6’s and 1’s will still be affected. Please note however, the choice to use the effects of the blunderbuss must be made before dice are rolled.