My RE keeps pads in the rooms so I just wore one there and threw it away when undressing and used a new one when getting dressed. You can take one with you if your RE doesn't have them. Also, I just cleaned up with the paper drape and balled it up so the blood wasn't visable with it in the trash. Then I went to the restroom in the lobby when leaving to make sure I was properly cleaned up. The RE who did my sono said it looked like I still had some bleeding to do since my lining was a little thick. Then she asked if I was still bleeding as she was taking the wand out and before I could answer she looked at it and said oh, yeah you are still bleeding, ok. Not my proudest moment... lol
ETA: I wrapped the old one in one of the paper towels they keep in the room to use after washing their hands. If your RE doesn't have everything in the room you'll need I would just take a purse and put some TP in it to wrap the old pad/tampon and some wipes to clean up with.