I ran to work for several years and am starting to get back into it again.
When I started, my schedule was to drive to work and drop off clothing and supplies on Sunday or early Monday morning. I ran to and from work Monday-Thursday. On Friday, I ran to work, packed up my things at the end of the day, and my wife picked me up on her way home. At that time, we had just one vehicle and I wanted to leave it with my wife during the week. Now, I drive on Mondays and Fridays and run both ways just three days per week.
Occasionally, someone offered to give me a ride home during bad weather or if I had to work late, but I only rarely accepted. If I really wanted or needed a ride home, I called my wife to come get me.
When I started, I had both a laptop and a desktop for work. I made the desktop my primary workstation and kept the laptop at home for when I was on call. Then, I carried a few things to work in a small fanny pack. My pack generally held my ID badge, my phone, and any goodies that my wife made during the week (scones, muffins, cookies).
Now, I have only a laptop. When running to and from work, I try to leave it in the office as much as possible. When I do need to take it home, I have an Osprey Talon pack. I think it is the 22L size. Whatever pack you choose, I recommend selecting the smallest size that will meet your needs. I like that it has a frame that allows some airflow between my pack and my body during hotter weather. It also has an integrated rain cover that I can use during wet weather. The downside is that it does chafe sometimes and most runs I find myself adjusting the straps throughout the run. That is why I leave my computer at work if possible and minimize what I commute with.
For me, doing laundry at work would not help so much since I also resupply with food each week. It might be nice if I could wash my running clothes right after I arrive each day. Instead, I wash my shorts and shirt with soap in the shower and hang them in my cube to dry so that they won't be stinky and wet when I'm heading home. My cube is set up so that my laundry is not obvious to all passersby.