One systematic review (1) conducted in 2003 examined the efficacy of several complementary and alternative therapies (including douching with sodium bicarbonate) for yeast vaginitis and bacterial vaginosis
Here an extract of their abstract:
Inconsistencies in definition of vaginitis, type of intervention,
control groups, and outcomes prevented performance of a meta-analysis,
and paucity of high-quality studies made ranking by evidence-based
scales unsuitable. Lactobacillus recolonization (via yogurt or
capsules) shows promise for the treatment of both yeast vaginitis and
bacterial vaginosis with little potential for harm. Boric acid can be
recommended to women with recurrent vulvovaginal Candidal infections
who are resistant to conventional therapies, but can occasionally
cause vaginal burning. Because of associated risks in the absence of
well-documented clinical benefits, douching remains a practice that
should not be recommended for the treatment of vaginitis. Finally, tea
tree oil and garlic show some in vitro potential for the treatment of
vaginitis, but the lack of in vivo studies preclude their
recommendation to patients for the time-being.
The second (2) was conducted in 2009 and examined the efficacy of probiotics (incl lactobacilli) for the prevention or treatment of three major urogenital infections: bacterial vaginosis, vulvovaginal candidiasis, and urinary tract infection.
Here the conclusion:
Overall, lactobacilli were beneficial for the treatment of patients
with bacterial vaginosis. No clear benefit was seen for candidiasis or
urinary tract infection. Studies were heterogeneous, with some limited
by a small population size. In conclusion, the use of certain
lactobacillus strains such as L. rhamnosus GR-1 and L. reuteri for
prevention and treatment of recurrent urogenital infection is
promising, especially for recurrent bacterial vaginosis
So to summarise, data suggests that probiotics (yoghurts with lacotbacillus) might be useful but larger studies are needed. Concerning douching with baking soda (ie sodium bicarbonate) or the use of hydroxide peroxide, evidence is sparse and their use is currently not recommended.
Here the summary of recommendations on UpToDate (a resource for health professionals)
There is no evidence from randomized trials that garlic, tea tree
oil, yogurt (or other products containing live Lactobacillus species), or
douching is effective for treatment or prevention of vulvovaginal
candidiasis due to Candida albicans.
As a side note, here an extensive review on the use on the risk of benefits of vaginal douching for women’s health.
Martino JL, Vermund SH. Vaginal Douching: Evidence for Risks or Benefits to Women’s Health. Epidemiologic reviews. 2002;24(2):109-124.
(1) Van Kessel et al.Common complementary and alternative therapies for yeast vaginitis and bacterial vaginosis: a systematic review. Obstet Gynecol Surv. 2003 May;58(5):351-8.
(2) Abad et al. The role of lactobacillus probiotics in the treatment or prevention of urogenital infections--a systematic review. J Chemother. 2009 Jun;21(3):243-52.
Sobel. Candida vulvovaginitis. Uptodate.com. August 2016