I've been super annoyed by trying to grab the scroll thing on the bar in a super long pdf. It keeps disappearing and on long PDFs where I want to scroll to, say, the middle, it disappears before I can precisely grab it. It's maddening sometimes.
I resort to the down key to make the scrollbar appear without losing my position in the doc. In fact, in Preview, my default workflow is to click on the main content panel as soon as the doc open; else the down key might take me to the next page, which defeats the purpose.
Why don't you just turn the scrollbars on permanently in System Preferences? It's under General > Show scroll bars always.