Bosium Strip

|Artifact| 3, T: Until end of turn, if the top card in your graveyard is an instant or sorcery card, you may play that card. If a card played this way would be put into a graveyard this turn, remove it from the game instead.
Forbid {1UU} |Instant| Buyback--Discard two cards. / Counter target spell.
Buyback appears on some instants and sorceries. It represents two static abilities that function while the spell is on the stack. "Buyback [cost]" means "You may pay an additional [cost] as you play this spell" and "If the buyback cost was paid, put this spell into its owner's hand instead of into that player's graveyard as it resolves." Paying a spell's buyback cost follows the rules for paying additional costs in rules 409.1b and 409.1f-h. See rule 502.16, "Buyback."
Are you asking if you can pay the extra cost or if you will get the card back if you pay the extra cost? The answer to the first is yes, you can pay the buyback cost of a spell when playing it through Bosium Strip. Will you get it back? Yes, if you want to. You have two abilities that both try to replace the "card goes to the graveyard" event, which means the controller chooses which order to apply them in. Then after you apply one ability, the other no longer applies and does nothing.