Been riding a Motorbike for over 20 years(600cc or above) only ever had one accident and that was in my car(and not my fault). Paramedics said if I was on the bike I would have been better off. Not arguing with that.
As already said motorists don't look properly and its not just for bikes the general standard of driving has fallen recently. But if the bike rider is aware of everything around him/her then they should spot problems before they happen.
I can honestly say I feel safer on my bike than in my car (nothing to do with the accident), as I can see everything around me and not trapped in a steel box if something does go wrong.
I've always felt like that even though I have driven cars a lot more than I have ridden bikes.
In my opinion, to ride a bike you have to have some sort of general interest in them in the first place as they command respect and as a commuting machine, winter can be a miserable time. Weather plays a big part in biking.
They are by no means death traps. If you do the proper training and don't rush into things, riding the bike should be pretty straight forward after a few miles out on your own. The problem is other road users. Where I am, bikes aren't all that common for some reason so other motorists just don't care to expect a biker in their daily drive. I myself have almost made the mistake of taking a bikerless route for granted when I very nearly pulled out on one.
The bike route is CBT (Certificate of Basic Training), theory test and then usually a course which takes you to your practical test (which is being revamped in October to be much more difficult). My advice would be to take your CBT, it's about £90 usualy and that allows you to ride up to 125CC with L plates for 2 years and then see what you think.
Costs are not all too bad. Budget for helmet + textile/leather clothing and boots, up to £500 for insurance if you're in a good area on a suitable bike and up to £3k for a young bike around 600cc and for a geared 125cc younger than 5 years you can pay under a grand however they might be a bit rough around the edges.
After adding it all up you'll find a small car cheaper and more comfortable however if you bought a mid-late nineties bike and sourced 2nd hand gear (but not helmet, always buy those new and make sure you get a proper fit in shop) you could find the costs more reasonable.