I have a similar-distance commute and have been interested in this same thing. Ditching my car insurance and registration will save me $1,300+ a year. (I'd still keep the car because it's at the age where cars stop depreciating anyways lol) Main issue being winter - how do you plan to cope with snow and ice on a two-wheeler? I'd be doing it with a motorcycle, but the principles are mostly the same - and the cost is similarly inexpensive.
I am in a pretty good spot with regards to winter. The city that I live in has an absurd amount of bike paths and they get cleared in the winter by the city. So when I wake up and go to work somebody has already scraped/salted all the bike paths.
I do plan on some nice "arctic" clothing and a winter-helmet with ear-protection. But that is about the extent of my planning. If I decide to go all-in then I might get some studded tires for my e-bike and change over sometime in November.
As for motorcycles: I know nothing of motorcycles, don't have a license for them etc. But here's my take anyway: A motorcycle has all the inconveniences of a car (insurance, repair bills, tire swaps) but does beat it on fuel-economy.
Now a motorcycle might the right choice in a lot of situations but I would prefer the e-bike if it is at all possible.
E-bikes have:
1. Low operating costs
2. Reasonable purchase price (compared to operating costs)
3. Does give you a bit exercise
4. No insurance required
And as a bike it can anywhere downtown, park almost anywhere and you can cut through parks (if allowed by local laws). It can also get through roadworks most of the time, drive through narrow alleys without a problem..
For distances of up to 15 km's I would recommend the e-bike over any other form of transportation (except normal bike) if it can be used safely.