Hi there! Interesting question and an interesting project
The Bonferroni correction issue is a very contentious one. As far as I know it is as appropriate to correlations as it so studies of group differences etc - but is it appropriate at all? If you run a search on Google Scholar you will probably find a lot of articles offering various sides of the debate.
A (very) quick summary thereof as I understand the pros and cons:
Advantage: Use of the Bonferroni correction can avoid situations such as an author examining 20 relationships, finding one that is significant at the 0.05 level, and claiming this indicates an important relationship (although a p value of 0.05 indicates a one in chance of a Type 1 error, so given no actual relationships in the population one would still expect one "significant" correlation). This doesn't stop unscrupulous authors from running the above analysis and then pretending that the "significant" relationship was the only one they were looking at all along.
In general the correction is a (yes, very) strict way to help avoid Type 1 errors.
-Use of the correction creates a paradox wherein if the above example involved 20 different studies each looking at one of the examined correlations, it'd be perfectly acceptable for each author to not use a Bonferroni correction (indeed, how could they?) - but if one author examines all the relationships at once, he/she is meant to use the correction!
-Use of the correction may exacerbate the problem of publication bias - cause more studies to have "insignificant" findings and therefore not be published, resulting in a greater literature bias towards larger effects and inaccurate metaanalytic findings.
-Much reduced statistical power
A couple of useful articles arguing against the Bonferroni correction:
Overall, the question avoiding occasional Type 1 errors really worth a much inflated Type 2 error rate? Using the correction helps ensure no Type 1 error is made - but also means you have a much greater chance of ignoring a relationship that is real (and maybe even important!) Imho the potential publication bias resulting from Bonferroni corrections making findings "insignificant" and the resulting bias of effect sizes in the literature as a whole is a far more worrisome problem than single studies making possible Type 1 errors. (Admittedly I may not quite be NPOV here!)
However... This may all be a bit academic, because actually I don't think looking at the bivariate zero-order correlations is the right way to select IV's to generate your final discriminant function. Why not use the discriminant analysis itself to decide which IV's to keep? As far as I know you can run DA's with all the usual types of statistical variable retention criteria - backward, forward, and stepwise entry, with a choice of alpha levels. This way you can select IV's that offer a statistically significant contribution to discriminating between the DV groups in the multivariate model. I suppose one could theoretically use a Bonferroni correction here to make your entry/removal criteria more stringent (can you? would you? anybody?) but I've never seen it done - Bonferroni corrections seem to come up more in bivariate analyses.
Hope this helps By the way - what is the actual theoretical bent of the analysis? I'm sure you're not actually trying to develop a measure to help librarians to decide which section books belong in