Is this nuts??

Hey there.
So...I've registered to run/jog/trot/amble/stumble a 5K on April 1st. My first ever. I am not a runner, and this will be a major challenge for me.
I've gotten into a M/W/F treadmill routine - 30-35 minutes of run/walk intervals. Last weekend, a friend and I went out for a <20 minute road test - run/walk on the road vs. treadmill - to make sure our legs didn't fall off (we did fine! :p).
All of this was fine and dandy when the weather stunk. This week is absolutely gorgeous. My biking nerves are firing like mad. I commuted today via bike (Tuesday). I would LOVE to get all the remaining days in this week on the bike.
So, that's my problem....
With turning the clocks ahead with Daylight Savings Time, I have plenty of light on the after work side of things. Would I be crazy to ride my bike in Wednesday (Thursday) and Friday, and on Wed and Fri head to the gym after work for a 1/2 hour on the treadmill right before I ride home? Would that be too much? The ride home is ~7 miles, which takes me about 40-45 minutes clock time (less "ride" time). Should I just keep up my running schedule until the event and not ride on my run days?
Thoughts? Thanks!