A purposeful walking pace is 3mph give or take, so half a mile is 10 minutes. Add a bit for road crossing etc. but from turning off your car engine to actually starting work should be under 15 minutes. You need a warm coat for cold days and a waterproof coat for wet days, plus decent shoes but can wear normal work attire.
A bike saves on journey time, your 10 minute walk might be 3 or 4 minutes cycle to cover the distance. But, get bike out of car, unfold if its a folder, put on crash hat plus whatever else you need to wear, arrive at work and put bike somewhere, often in a shed or basement, lock it to something. remove your bike kit. I bet it will take longer, plus you need to buy a bike and bits of kit and maintain things.
Cycling is good for longer trips. but the faff at each end means that walking is probably the best way to do it if it's under a mile. Plus if you are walking you can easily pop into a shop en route should you need to without any bike thieving worries. Plus walking can be companionable if occasionally you run into a colleague on the same journey.
Maybe try it for a bit before you invest in an alternative.
