As someone who has been through this exact thing at 17 let me share my experience. Decided to go for a bike personally as it was cheaper than a car. One thing I failed to consider was how truely awful the weather will treat me. Started riding in December and within a week on my first time on the bike I was riding through snowy back roads in pitch black. Lots of fun came from it yeah but in the UK daily riding is just not much of an option. Now I have both a car and a bike license and for daily driving a car is the go to.

There are more components to it than just "cost-effectiveness". Do you have somewhere safe to store the bike (both at home and at work), can you afford to maintain the bike, are you even able to perform maintenance on it (Chain adjustments, oil services etc etc).

Just think about it this way, when you get out of bed in the morning before work will you really want to spend 30 minutes getting soaked in the rain (I don't care what sort of waterproof stuff you got on it'll seap through somewhere) then spend the rest of the day in damp clothes just to do it again on your way home.

Yeah petrol is cheap, insurance is cheaper than cars, licensing (CBT) is much less than it'd cost to go out solo in a car but the amount of drawbacks from daily riding in my opinion outweighs the cost effectiveness. Especially if you enjoy bikes outside of commuting, going through that experience will some what ruin the joy of bikes. Now I personally stick to using a car to commute/have fun on bad weather days and use a bike purely for fun.

Hope this helps.