That rule of thumb uses the number of cases in the minority group, in this case 25 in B. So you have about 2 events per variable†: you can still use logistic regression, but your model is likely to grossly over-fit the sample data—use bootstrap validation or cross-validation to estimate the consequences (or use the heuristic shrinkage estimator described here).
Collecting more data would be a very good idea. You might want to reflect that the 95% confidence interval for the overall proportion of B is roughly (0.13,0.26), so you can't hope to learn about the individual effects of each of those 12 predictors with much precision at all. If you really need to build a predictive model on this sample, carrying out data reduction on the predictors would be sensible—try to get the number down to about two or three. Regularization is an alternative way to improve predictive accuracy.
† It's in fact events per regression degree of freedom you need to consider; so each dummy variable for a categorical predictor, each polynomial or spline term, counts.