Even if work and home tasks are separate, your GTD system needs to track both.
I struggled with the same issue and ultimately discovered that using GTD only at work--doesn't work. In order to realize the benefits of getting your to do list out of your mind and into a system, that system needs to capture everything. This means whatever single system you use to maintain your context lists (electronic, paper, etc.) it needs to contain all your next actions and projects in every facet of your life.
This admonition is totally consistent with a work/life balance that keeps work almost exclusively at the office but makes time for "home" tasks like paying bills at work.
I use Remember the Milk. I have locations set up for @work and @home (@ is RTM notion for a location), and most new tasks are associated with one of those locations. Additionally, I use tags for items that require the internet #@web and #@call (# is RTM notation for a tag). (Bit of an aside, but a task can only be assigned multiple tags, but only to one location.)
My context lists are really smart lists based on search queries. My work list pulls up all tasks not intentionally deferred to a future date that are assigned the @work location, or that are tagged @web or @call.
(list:inbox AND (dueBefore:Now OR due:never)) AND (location:@Home OR tag:@call OR tag:@web)
A similar query builds my @home context list.
If your bills are personal tasks that you are definitely going to do at work then tag them to show up on your @work list; you've made the decision to perform the action there, your context lists should reflect that decision. If it's something you could do at home or work and you don't care which, then use a tag that shows up in both your work and home context lists (e.g. my @web tag).
This enables you to use a single tool to track both personal and work tasks, but to keep them in separate lists so you're only presented with tasks that your in the right physical place to perform.
Lastly, ubiquitous capture enables you to add a work task to your system from home, and vice versa. The ability to capture a task whenever it occurs to you and assign it to the right context frees your mind to concentrate because it knows your system will remind you of the action when you're in a position to actually do something about it.
8GTD doesn't distinguish between work and home tasks. They are tasks and projects that need to be done. – Brian Carlton – 2011-06-22T20:37:25.693