Leaving the saran wrap for 4 or 5 days is the regular thing to do here. I've read it several times on different tattoo sites on the internet and it's also what my tattoo artist told me.
You leave the first wrap over night, then you take it off and wash the tattoo every morning and evening, then put some ointment (strange word, I looked it up, never heard before) on it and wrap it again.
I've been told that the saran wrap keeps the tattoo from developing an eschar.
Makes sense to mee. Additionally, the ink bled the first 1.5 days. Would have soiled all clothes without the wrap. But maybe this is because of the not-so-thin, solid black line I have. I think the other lines from the tattoo didn't bleed (much).