Maybe head somewhere quiet if possible, like a woods or something similar where you might see someone, but chances are you will not. (I hope although it is public, it is only your dislikes and also low chance of being seen, if it is too far i will rework a dare for you!)
Wear a skirt and a pair of small panties (Hopefully small enough to comfortably fit in your mouth). The rest is up to you. Take a bag with some toilet paper in it incase you feel the need to clean up, and if it makes you more comfortable maybe a change of underwear or a pair of shorts just incase.
About an hour before you plan on going, drink 2 litres of water (Or until you cannot drink any more). Just as you are about to leave drink another litre if you can. Head to the place you will complete the dare.
By now you should really need to piss. Put your headphones in and listen to
this or something similar as you walk. You might start to trickle a little piss as you walk whilst trying to hold it in, but you are not allowed to find somewhere to pee until the video is up. You must stay on the main path as you walk too.
If you make it to the end of the video, you may find a nice secluded spot to go pee. Do it through your underwear so they're nice and wet. You can now walk back, either wearing your wet panties, or with them stuffed in your mouth.
If you failed, well then you have left a nice piss trail along the floor behind you. You must now put the panties in your mouth and walk back with them.
To modify it you could clean up any dribbles on your thighs, or leave them so you can feel how slutty you are, or you can put underwear on so you are not commando.