Unclogging a bathroom sink without removing the P-Trap

Hi all. Anybody have any tips or tricks on making a bathroom sink drain faster without going through the process of taking it apart, cleaning it, and putting it back together?

Normally when my bathroom sink starts to drain slowly, I remove the P-trap and push all the gunk through the bottom into a bucket using a metal rod. Now that I might be responsible for cleaning out several bathroom sinks, I'm starting to dread this process far more.

Drano works OK and makes the sinks drain a bit faster, but it usually gets bad pretty quickly again. Any tools I should be investing in for minor stoppages like this?