Generally you want to give buffs over to the person who is going to make the most impact in the game with them. Most people give blue to casters and mages because it helps them do more for your team than you, as a jungler, may be able to do with a blue buff (ie. it's more useful on them than it is on you). Likewise, red buff is typically given to AD carries because they have the range and AA to get the most use out of it.
As for your situation, you can also just take it for yourself. Blue buff isn't going to do much good on a caster who gives it up immediately. At the same time, if you give it to someone who doesn't die, but doesn't really do anything for your team, it isn't going to do you much good either. It's about maximizing impact with the resources you have.
Alternatively, Blue buff can be pretty useful on AD carries, especially Ezreal/Corki, and can also be good on manaless champions like Zed and Riven.