Healing out tattoos can be a bit tricky. If you have had good success healing tattoos a certain way in the past feel free to continue in that manner. Otherwise here is a simple method to healing your tattoos...
Leave your wrap on for a MINIMUM of 3 hours, but don't exceed 24 hours. I know you are excited about your new tattoo and want to remove the bandage to show it off, but it will still be there when its time to remove the bandage. Taking off the bandage too early can result in problems with the healing. In most cases I suggest leaving it on until you are ready to go to bed that first night.
After removing the bandage you should wash the tattoo carefully with a mild hand soap: I recommend Dial and warm water. The warm water will open up the pores and allow any elements from the tattooing process to be cleaned out. While the warm water is key to the cleaning process, it is also important to close the pores after cleaning. I suggest running some cool water over the top of your tattoo just before finishing up.
Once your tattoo has been cleaned of all surface elements, pat dry the area, and allow to air dry for approximately 15 - 20 minutes. After the air drying apply a VERY THIN coat of Polysporin. You may blot off any excess ointment with a clean paper towel.
Follow this cleaning regiment a few times a day for about two to three days, just until the tattoo begins to feel hard. The tattoo will then begin to flake off.
After that you will need to continue to wash your tattoo several times daily and apply a non-fragrant lotion: I recommend Lubriderm or something similar.
Of course you will also need to keep the fresh tattoo out of all submerged waters; baths, pools, jacuzzis, the ocean, and all direct sunlight, as well as dirty surroundings.
Your tattoo should be cared for properly. You spent good money on it, as well as your time. Don't waste it by slacking off on the aftercare.