Save your homepage as a bookmark, either within the browser or on to your PB desktop. Then you can access it anytime. Also if you type the first letter or two of the homepage in the address bar the browser will auto-suggestions it (once youve been there already).
Have you set your default homepage in Options? If not, when in the browser, swipe down from the top bezel and choose Options. Also make sure that your homepage is the default choice for new tabs. Then anytime you open a new tab (the square next to the forward and back arrows in the upper left corner of the browser), you'll automatically go to your home page.
There is no direct way like pressing the "H" key. Also if you only have one tab open and you press the tiny, little, X, it will close your current site and reopen your homepage.