It is forbidden to buy things on Shabbat and Yom Tov, either because the navi[1] warns against “looking for your interests and speaking matters” on Shabbat or because commerce may lead to writing.[2] On the other hand, the mishna[3] permits acquiring items, even from a professional proprietor, on Yom Tov and Shabbat.[4] This is permitted if the product is intended for use on the holy day and the acquisition is done in a way that avoids classic signs of commerce.[5]
What must one avoid? One of the major issues is measuring quantities[6] or, under certain circumstances, even using a measuring utensil without actually measuring.[7] This problem is not relevant in your case, even if the baked goods are sold by weight, as the measuring is done before Shabbat.[8] There is generally a prohibition to mention the purchased item’s price when discussing its acquisition or to use a term such as “buy.” (One can request that the provider “give” or “fill up” or say that he wants to “have” or “receive.”)[9] This is obviously not a problem in your case, as the “acquirer” on the honor system does not need to interact with a supplier.
One might argue that since the price is listed, it may still be considered a forbidden sale (especially since the buyer is acquiring the food in the same basic manner it is done during the week[10]). In truth, however, the fact that the price is listed is not a problem. In fact, the Rama[11] uses the existence of a known set price as a mitigating factor. In discussing what one should not say, the gemara mentions the idea of s’chum, which usually means a total. The Rishonim dispute whether it is permitted to mention the measure of a specific item that one is acquiring without adding it to previous purchases to arrive at a sum total. The Rif permits asking for a certain object at a certain price as long as one does not add up the various obligations.[12] The Rama accepts this opinion, provided that the price is known. In that case, the mention of the price is viewed not as a commercial discussion, but as a means of identifying the amount of product that one wants.[13] Although the poskim question whether we should rely on this leniency,[14] it is clear that the fact that a price is clearly known does not render the transaction forbidden if it is not mentioned orally. The Shulchan Aruch,[15] whose stringent opinion is accepted by Sephardim,[16] rules that a price should not be mentioned in any case, but even he does not object to an object’s price being clearly known when agreeing to the transfer.
One thing one must avoid is studying the price list, as detailed written accounts of transactions are known as shitrei hedyotot and are forbidden to be read.[17] (In that context, the Mishna Berura also points out that one should not put pins next to the name and amount of money that corresponds to the details of the transaction. It is possible that the pin or similar system can be used for mitzva purposes, such as recording pledges at a charity appeal,[18] but that is beyond our present scope.)
Although issues of Shabbat do not prevent taking the baked goods on credit, one should make sure that the proprietor allows him to take them, since he is not able to immediately write down his debt. It is possible that the seller trusts his clientele not to lie but does not to trust them to remember to update the account after Shabbat.