Yes you can. Both Bitterblossom and Contamination trigger at the beginning of that player’s upkeep. When Bitterblossom’s trigger resolves, there is a round of priority where each player may cast spells or activate abilities. At that moment you may activate Vedalken Shackles and steal their new token assuming it meets Vedalken Shackles’ requirement of power being less than islands.
October 6, 2018 6:38 p.m.
It's your turn and you control Contamination and Vedalken Shackles. An opponent controls a 1/1 token. It doesn't matter if the 1/1 was created by an opponent's Bitterblossom in this situation - that trigger doesn't come into play on your turn, it triggered on your opponent's turn (otherwise you wouldn't need to steal the token).
Contamination's triggered ability goes on the stack during your upkeep. You can respond to it by activating Vedalken Shackles to steal the token. You will control the token when Comtamination's trigger goes to resolve.
Instead, if you control both Bitterblossom and Contamination, you can stack the triggers such that Contamination is at the bottom of the stack, and Bitterblossom is at the top. Bitterblossom will resolve first, and so generate a token before Contamination requires a creature to sacrifice.
If instead, an opponent controlled a permanent with "EACH upkeep, create a 1/1 token" you could still do this. Opponents' triggers are put onto the stack after yours during your turn; they will resolve before yours. Thus the 1/1 will be created before your Contamination tries to resolve, during the round of priority before you go start to resolve it, you can activate the Vedalken Shackles to steal the token.