What is purpose of sulfuric acid in iodine extraction?
You need a strong acid to provide hydrogen (technically hydronium) ions, which is true for most aqueous oxidation reactions:

$\ce{2I- +H2O2 +2H+ -&gt; I2 +2H2O}$

Unfortunately, bisulfate ion appears to be a weaker acid than water $(K_{\mathrm{a}} =  10^{-2})$, so it may not work unless you use a very concentrated amount to obtain enough hydrogen ions. Try it!

A fairly cheap alternative could be hydrochloric acid, which may be available in hardware stores as muriatic acid, and is stronger than sulfuric acid. But read the MSDS, as hydrochloric acid fumes and is nasty stuff.

Best of luck, it’s a cool experiment!