It says in the Mishnah (29b),
הולך אדם אצל חנוני הרגיל אצלו ואומר לו תן לי ביצים ואגוזים במנין שכן דרך בעל הבית להיות מונה בתוך ביתו:
This as well is paskend in Shulchan Aruch (Siman 323 Sif 4) and says there as long as he doesn't mention the price.
My question is, without mentioning the price why is there still not a gezera that maybe the store owner will write down how much the person took?
Yehoshua, Yerushalayim, Eretz Yisrael
This is a very interesting question! I have not found anyone who asks it explicitly, but we can think about it logically and come up with an answer.
1. Rashi (Beitzah 37a, DH Mishum) writes that one of the reasons why Mekach u'Memkar (business) is forbidden on Shabbos and Yom Tov is that "Asi l'Yedei Kesivah" -- one might come to write things down. However, I think we learn not only a Chumra from this Rashi but also a Kula, namely that not only if an activity is considered as business is there a concern that one may come to write on Shabbos as a result, but conversely if an activity is not considered Mekach u'Memkar we may be lenient and say that Chazal would not enact a Gezeirah lest one come to write.
2. Now, if we look at the Din in Beitzah (29b) we notice, as you pointed out, that the storeowner must not mention the price. We also observe that the Mishnah states that the reason he may say how many eggs he wants is that it is the normal practice that a householder counts in his house how many eggs he needs. The Ran writes that, consequently, it is not obvious that when he mentions the number of eggs to the storeowner he is doing so in order to know what the price will be. Again, we see that Chazal were careful that this activity should not fall into the realm of business.
3. In addition, the Mishnah states that it must be a storeowner whom he frequently visits. This ensures that there is trust between the seller and the buyer and it will not be necessary to record the transaction in writing because even if the storeowner forgets how many eggs he sold, the customer will remind him.
4. Furthermore, the sale of the eggs in the case of the Mishnah is not done in a way that implies that the buyer will pay back only a long time later. If it would be done that way, then there would be a Gezeirah that the storeowner might write it down, as we find in Shulchan Aruch (OC 207:11) that one may not ask his friend, "Halveini," because this word implies that he has a long time in which to pay back. Rather, one should say "Hashileini." If this transaction is being done in a language where the above distinction does not exist, one should say "give me" which does not imply that he has a long time in which to return. This is the phrase used in the Mishnah, "Tein Li," and therefore there is no Gezeirah that the storeowner will come to write.