Can I take a hydrocodone 500mg and naproxen 500mg together?

Why bleeding? Hydrocodone is an opioid analgesic that ordinarily would be safe to use with a NSAID such as naproxen but I see in your history mention of "bleeding". Although rare, NSAID's might increase the propensity for "bleeding" depending on why you are "bleeding" and where you are "bleeding" from. To be on the safe side you should chat with your MD about whether or not using an NSAID would be safe for you!
See details. What do you mean by 'bleeding?' If you have any issue with bleeding you should not take naproxen.