Yep, use caustic soda crystals. It's the best unblocker I've used and won't rot the pipes. You can buy it in any hardware shop by the half kilo and just keep it next to the bath. As soon as it starts to drain slowly stick some down and it'll clear it through in minutes.
In this case I'd pour a cupful of dry crystals straight through the water down the plughole, but expect it to bubble, fizz and burp a bit.
It's sodium hydroxide so if you get it on your skin wash it off with water immediately and be careful to keep it away from your eyes.
trust this guy, he is the future Robbie Rocket Pants! How are your rocket based adventures going btw?
B@