For a charitible contribution that was a bargain sale, does one enter the "value" as the appraised value, or the difference between the value and the bargain sale amount?

1. The donation value is the value when donated. What would someone else pay for the item that day or the stock value. For items that require an appraisal, see here. Here are some common items that do not require an appraisal and how to value them with thrift shop or consignment shop being common valuations.  Publication 561, Determining the Value of Donated Property states:

Household Items

The FMV of used household items is usually much lower than the price paid when new. Household items include furniture, furnishings, electronics, appliances, linens, and similar items. Household items do not include paintings, antiques, objects of art, jewelry, gems, and collections like stamp and coin collections. Such used property may have little or no market value because it may be out of style.

You cannot take an income tax charitable contribution deduction for household items unless they are in good used condition or better. The one exception to this is a household item that is not in good used condition or better for which you claim an income tax charitable contribution deduction of more than $500. In this case, you must obtain a qualified appraisal valuing the item and complete a Form 8283. See Deduction over $500 for certain clothing or household items, later.

If the property is valuable because it is old or unique, see Art and Collectibles, later.

Used Clothing

Used clothing and other personal items are usually worth far less than the price you paid for them. Valuation of items of clothing does not lend itself to fixed formulas or methods.

The price that buyers of used items actually pay in used clothing stores, such as consignment or thrift shops, is an indication of the value.

You cannot take an income tax charitable contribution deduction for an item of clothing unless it is in good used condition or better. An item of clothing that is not in good used condition or better for which you claim an income tax charitable contribution deduction of more than $500 requires a qualified appraisal and a completed Form 8283. See Deduction over $500 for certain clothing or household items, later.

2. The program asks for your cost basis to follow the rules. Enter the amount you actually paid. Your donation may be limited by your original purchase price for some things.

Reference: Topic no. 506, Charitable contributions