1) The Steipler Gaon zt'l was asked about this הגהות הב"ח and he replied (reported in Peninei Rabeinu ha'Kehilos Yakov, vol. 2, p. 19), "It is as clear as the sun that this is not the Hagahos ha'Bach, and the Bach did not write it. It was written by a student of the Bach who did not remember the verse. He thought that the verse was written without a Vav, so he made an amendment and erased the Vav...."

2) See also the Shi'urim of Rabeinu Meshulam Dovid Soloveitchik zt'l, the Brisk Rosh Yeshiva, on Maseches Nazir, 23a, p. 216, Shi'ur #57, who writes that it is צ"ע on the הגהות הב"ח since the verse reads וצדיקים and in addition the Gemara in Horiyos 10b (where the Gemara also cites this verse) also reads וצדיקים and there the Bach does not make any amendment. Rav Dovid leaves his question on the Hagahos ha'Bach unanswered.

3) However, the elder brother of Rav Dovid, Rav Yosef Dov zt'l, also Rosh Yeshivas Brisk, is cited in Chidushei ha'Griz (the Chidushim on Nazir of his father, the Brisker Rav zt'l), p. 102 (DH Gm' Mai) as giving an answer to this question on the Bach, based on what his great-grandfather wrote, near the beginning of the introduction to Teshuvos Beis ha'Levi (end of DH Amar ha'Mechaber), that the reason we often find in Shas that verses are cited in a different way than they appear in Tanach is because of the Halachah (see Gitin 60b), "One is not allowed to say verses from the Written Torah by heart." Therefore, in the time of the Gemara, when they used to say a verse from Tanach they would read it from the Written Torah. However, sometimes it happened that they did not have a book available at the time they wanted to mention a verse, so they would say the verse in a slightly different way than it is written. If it is slightly different from the original, one is allowed to say it by heart. This is why the Bach changed the word in the Gemara and made it read without a Vav.

4) I should add that I asked a friend, who is familiar with different texts in the Mesorah, to check if he can find any texts in Hoshea 14:10 that read without a Vav, but he replied clearly that there are no such texts, so we must remain with the answer that the Gemara changed the text of Hoshea, and it is not the original text.

5) Following the approach of Rav Yosef Dov Soloveitchik zt'l, I have found, bs'd, texts in the Gemara that support the Bach, and texts in Tosfos (in this particular instance, and also in general concerning the way the Gemara quotes the verses) and other Rishonim and Acharonim who cited our Gemara without the Vav of Tzadikim:

a) The Dikdukei Sofrim in Horiyos 10b, p. 32, cites a text which reads Tzadikim without a Vav. In his footnotes, the Dikdukei Sofrim writes that most texts read with a Vav, but at least we have found a bonefide text of the Gemara that cites the verse without a Vav. The Dikdukei Sofrim in Bava Basra 89b, where this verse is also cited by the Gemara, also cites a Girsa which reads without a Vav. Again, the Dikdukei Sofrim writes that most of the texts read with a Vav, but we have now achieved finding two texts in the Gemara without a Vav.

b) I also argue that the fact that we found a text in Horiyos 10b that omits the Vav means that we may suggest an answer to the question of the Steipler and Rav Dovid on the Bach from Horiyos, because the text of the Bach in Horiyos follows the text cited by the Dikdukei Sofrim there without a Vav.

c) Now we go, bs'd, to Tosfos in two places where his text also omits the Vav. Both places are where the issue discussed is Achilah Gasah, as it is in Nazir 23a. The first source is Tosfos in Yevamos 40a (DH Achilah) where Tosfos cites our Gemara, and cites the entire verse (not a shortened version) and the Vav of Tzadikim is omitted. The second Tosfos is in Bava Kama 110a (DH Achilah) where Tosfos again cites Nazir 23a and reads Tzadikim without a Vav. There, Tosfos does not cite the entire verse, but the Hagahos ha'Bach #4 cites the beginning of the verse, and again Tzadikim is without the Vav. I argue that the fact that the Bach goes out of his way to cite the fuller verse without a Vav, shows that this is indeed the opinion of the Bach, that the Gemara cites our verse without a Vav.

d) I also found that the Ibn Ezra (Mishlei 10:29, on the verse "Ma'oz l'Tam") also cites Tzadikim without a Vav. The Ibn Ezra was a contemporary of Tosfos (see Tosfos to Kidushin 37b, DH mi'Macharas who cites the Ibn Ezra), but one would not normally identify him as being independent of Tosfos, so we now have another independent source in the Rishonim for the Girsa without the Vav.

6) On a general note, we find that Tosfos (Shabbos 128a, DH v'Nasan) writes that the way of the Shas is to shorten, and say in a different shorter way, the verses that it cites. This is a source for what I wrote above (in point 3) and also means that it is not so surprising that Tosfos in Yevamos 40a and Bava Kama 110a omit the Vav. We also find in Berachos 2a and 4b that the Gemara cites "b'Shochbecha" and not "uv'Shochbecha" that is written in the Torah. So we see that the Gemara sometimes makes the verses shorter by omitting only one letter.

7) I will now, bs'd, cite other Rishonim and Acharonim who omit the Vav, and I argue that in many cases this is because they are following the approach of Tosfos. First, see the Rosh (Bava Basra 5:26 (he is in fact referring to the Gemara 89b that I cited above in 5a) who omits the Vav. We know that the Rosh very often follows Tosfos. See also the Bartenura and Tosfos Yom Tov on Kelim 17:16 (this Mishnah is in fact cited in Bava Basra 89b) who both read Tzadikim without a Vav.

8) I will conclude that it seems that the Maharsha always cites the verse without the Vav. The first place is the Maharsha in Bava Basra 89b, where there is no Vav. The Maharsha in Bava Metzia 83a also omits the Vav. The Maharsha in Yoma 29a (DH Hirhurei) is also without a Vav. And finally, if we look at the Maharsha to Horiyos 10b (which we have noted before was one of the places from which the Hagahos ha'Bach was challenged) we notice that on both occasions that the Maharsha cites this verse (DH Pesach, DH A') it is without a Vav.

גל עיני ואביטה נפלאות מתורתך!