Call or visit the permit office. They will give you an idea of costs and time.

ppf is right. Don't do it without a permit. It creates huge valuation issues of your property as the value of the second bath can't be used for appraisals or for selling purposes. Plus code enforcement can get involved. Look up the penalties in your area for building/remodeling without a permit. If you were to sell later - doesn't matter how long later - it becomes a huge liability for the buyer if you manage to sell it without disclosing and the buyer can come back against you for non-disclosure and unwind the deal. It just isn't worth the risk, You get so much more value when you do it right.