It would be unusual for any bars to ask for ID unless they wanted to make an excuse not to let you in,ie: if you wobbled towards the door.
Clubs may do but again if you arrive fairly early and look the part you should have no trouble anywhere in Ibiza,have a great time,John.
P.S.Most establishments would not expect you to carry your passport around with you but the police will as its the law.They will usually be quite happy with a photo copy so take one with you as it might save you a night in a cell awaiting confirmation of who you say you are........