It may sound silly, but I wish to know if I can use both wordfence security plugin and bulletproof security plugin together.
These are plugins just like any other and they may or may not work together well. Their performance may also be affected by the theme you use as well as other plugins that you have installed. The only real way to find out is to try them both.
You can also try Googling both of them along with the word "conflict" to see what results you get.