I recall when I was your age everyone told me that these would be the "best years of my life". Balderdash (what an antique epiphet). Your predicament is predictable and it is one of the benefits of being an adult.
I sympathize with your frustration at missing the prime riding season this year. Many of our posters seem to miss the idea that riding a bike in Toronto in say January is less than ideal.
I can sympathize with your mother. But she has not been entirely consistent. She seemed to leave the issue of getting a loan open when she mentioned that you did not have a job and now you have one, well you can make the money yourself. She is not consistent but then again many people are not. Think about it, being a parent is hard work and most parents make mistakes. If she does a good overall job, well you need to cut her some slack no matter how frustrating she seems right now on this particular issue. This is not really something that is big enough issue in my opinion to really cause a big fuss over. She will be your mother for the rest of your life so try to remember that.
On the issue of danger, well your mother is misinformed. My mother worries about my riding and I have given her the safety statistics on cycling and I am 50 years old! In your mother's support, I often don't FEEL entirely safe when I am riding even though it is safe.
As for the price of a bike. You mother is probably thinking the old "paperboy" special. She really does not know the difference a high performance road bike makes. And you might not be able to educate her on this one.
This information probably will not help you, but I hope you can understand that your mother is not being entirely unreasonable from her perspective.
By the way, in your mother's situation, I would give you the loan with a specified payback plan. Your getting good grades and having a job show responsibility. But then again, I am a cyclist and I understand your situation. If I had a kid who wanted a set of drums or something like that, that I don't understand, I could be just as blockheaded, I suppose.
As to the messiness of a bike in your room - you can possibly take steps to store your bike in your room without making a mess such as putting a rack up and putting something like a drop cloth on the floor to protect it.
Still that does not solve your current problem.
Other posters have made some suggestions.
1) Buy the bike on time from the bike shop.
2) Wait and buy later.
3) But a cheaper bike.
4) A new one - buy a used bike.
I think in order of desireablility it would go 1 then 4 then 2 then 3.
Good luck with your problem.