i started my ~9mi round trip commute around april of this year. last 4 months or so I've pretty much not missed a commute unless I knew I had to be at a jobsite after I got in the office. When I first started I felt like 15mph was 'really fast!' and 12-13 was pretty normal. 6mi at that speed would be ~1/2 hr. You'll still feel like you're hot stuff -- looking at the way kids on their bike go to school, we were probably going 10 or so back in the days, and the jump in speed will be noticeably different.

You'll definitely get faster over time, and the more you understand road hazards the more you'll feel safe about being on the bike as well. Definitely reward yourself with a snack or something when you do the commute, and give it a try for a while. Pretty soon you'll be wanting longer commutes, making up 3-4 patterns for different length routes before and after work.