My pleasure. I think a lot of people end up doing transportation-related things as the result of this kind of curiosity. In my case, I got serious about bicycle and pedestrian advocacy as an undergrad after a beloved professor was killed crossing a street by hit-and-run driver. It took me nearly a decade after that to decide to do a masters in planning. Then the research bug bit!
Planning is belligerently multi-disciplinary. Provided you can spin a good yarn in your entrance statements, and your CS GPA wasn't in the toilet, having a CS degree is a fine asset.
One thing to think about (beyond "do I want to enter a field in which I will earn less than what I'd make with a CS degree alone?") is how you want to come at transportation. For example, sometimes people ask what the difference between a planner and a civil engineer is. I usually reply something along the lines of "if you want you build a bridge, call a civil engineer; if you want to know where to build a bridge, call a planner."
Planning, civil engineering, and public affairs all have their fingers in the transportation pie. If you're a planner, a masters program will try to prepare you for a pretty broad range of tasks that include knowing something about your problem domain, how to communicate with political types, and how to communicate to angry citizens with pitchforks.
Civil engineering tends to focus more on nuts and bolts kinds of problems in transportation. Oddly, I feel like civil engineering is more solidly represented in statistical modeling functions within planning agencies. I.e. civil engineers tend to be more quantitative. That said, I always had the option of taking courses cross-listed with statistics--the same coursework that is now making my brain bleed in the PhD program.
Planning tends to be more systems-oriented at the technical side, and more human-oriented at the drum circle side. The differences between public affairs and urban planning can get pretty minor at times--my masters program offered concurrent MUP with public affairs (and maybe civil?) options. I knew a number of students who did public affairs and planning.
My feeling (perhaps erroneous) is that planning masters students get a little more latitude to play than do civil engineering masters students. There are planners that do lots of different kinds of stuff--even just within transportation planning, never mind land use (more important than transportation), electric, sewer, water, etc. As a result of needing to do lots of stuff, you get more freedom to scratch your own itch. That said, getting a job with your masters in civil and PE is likely a bit easier than as a planner. But, you've already got a job-friendly degree ;-) For the record, I had an easy time getting work as a planner after my MUP, but I did have classmates who took a little longer to find relevant work.
My recommendation before going and upending your life for another degree would be to go read some good mass-market books that explore basic concepts and contemporary issues in transportation planning. In order, I'd suggest Traffic by Vanderbilt, The High Cost of Free Parking by Donald Shoup, and Human Transit by Jarrett Walker (disclaimer, I had a minor role in reviewing the latter). All three are written with a minimum of jargon, and all three will give you a flavor for the kinds of things planners think about. You might then find out if your city has some sort of group that meets to hack for civic purposes. These are cheap ways of scratching the itch...