Could I do just do R to Z fisher transformation and then do anova of the Z values? If I do this, should I use bonferroni correction?

You can just do the calculation for one correlation at a time and use the Fisher transformation to find out the standard error for that correlation. Then you take the next correlation. You can do that with a pocket calculator.

If you want to compare two korrelations, say corr1 and corr2, or take the difference between them, like

corr1 - corr2

The "uncertainty" in that difference can be:

(corr1 - corr2) +/- 1.96*Sqrt( std(corr1)^2 + std(corr2)^2)

(That would make the strong assumption that the two are not dependent, but maybe this is good enough.)

A possibility is to do bootstrap simulations, but maybe that is too difficult.

Or maybe you can formulate the problem as an anova problem (like the other ones suggested), not dealing with the correlation coefficient at all.