You could also consider investing in a uv sterilizer that doesn't require any washing or drying. The units are a little bulky but they can probably be hidden away under your desk. They're also about 2-3x the price of an electric steam sterilizer but for the ease and convenience at work, it sounds amazing. And probably better (and cheaper) than investing in a 2nd pump just for work. This blog is a good resource: http://mlbb.com.sg/into-the-world-of-uv-sterilizing/
I've seen my colleague simply rinsing hers with hot water after she pumps, shaking it and leaving it out on her desk (she has a small drying rack) to air dry before the next use. Also saw another one who will keep hers in a ziplock after washing. I think rinsing with hot water is the common practice. ;)
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I rinse them with hot water and put them back into the airtight container which stored in the fridge. I sterilize at night. I have colleagues who prefer to bring a sterilizer to work too.
I actually never wash my pumps at work. I just store it in the fridge till my next pump session and then rinse it and sterilize it when I get home.
after pumping I will use hot water to sterilise them then keep in a zip lock bag.. after which I keep them in my cooler bag..
No need to wash it right away, just store the milk in a cold place and wash it well at home.