Good old neatsfoot agreed!! What i do is get an ice cream tub or something similar and fill it up with it ( only a couple of inches) if that makes sense. Then just stick your bridle in there and leave it overnight. Works for me!!!
Sorry but if its a new bridle for £30 with reins then the leather may never get supple as it is likely to be poorer quality. You also have to be careful with cheap leather that you dont over oil it, as this will promote tearing and it weakens the fibres. Balsam or ko cho line would be safer