We're kinda in the same boat, only that I'm not living with my parents anymore and I'm old enough to go wherever I want to go..
I came out as a furry about a month ago, and my mom asked me about it and I explained it as well as I could, making it perfectly clear to her that you can ask "what's a furry" from thousands of people and get thousands of different answers.. There are bad sides in all fandoms, but people kinda seem to like to forget that since furries in my experience seem to be prety open with their fetishes.. But that still doesn't mean everyone is into that sort of stuff... Mom didn't really get it, and didnt' show too much interest, but a few days later her boyfriend was driving me back to my placce and he suddenly started to ask me stuff about the fandom, what it was all about and stuff... He was really understanding and showed quite abit of interest.. Hopefully he
can bring my mom to understand it better too...
I havn't told mom about me getting another fursuit tho, since she weren't too excited about it last time i got one (that one was a gift for my pet fox.. Now it's finally my turn), since I'm worried about how she'll react...
But at least she accepts that im a furry and doesn't seem to see it as anything weirder than "a bunch of grown up people who like to dress up as animals and have fun"
What I would do in your situation is to try and tell your mom that the media have only targeted the "bad part" of the fandom since that makes for more interesting and better-selling stories than "David, 25, likes to dress up as Kevin the fox and party with his friends".. The bad part is there, but it's not the main thing in the fandom for most...
And not caring about what other people think of you is a great thing.. It's those who try and be just like "everyone else" who are the weaker ones in that case
As for sexuality, is it really necessary for your friends and family to know that? I also have some really confusing things going on in my head about "what i am", but I don't feel like my family or friends need to know more about it... (I have pretty accepting parents tho since one of my siblings are currently in a same-sex relationship and my parents accept it quite ok.. Event tho they "wish it wasn't that way" they can still live with it and be supporting)
If you still think you want to come out with it, remember that there's nothing wrong in being bisexual or anything else no matter what people say or do, and if they can't accept it, the problem is on their side.
I can't really relate to the last thing since I've let my parents down too much when it's about school so they've kinda given up on me there... But I think trying to tell them how you feel about it could help...
And yes, if you think your mother will accept and understand you, try find some time where you both will have plenty of time to talk through things alone.. You don't need to tell her everything at once, but just get the whole thing started so that she knows what's going on in your head..
^That's at least what I have tried and what I would try... I'm not all that good at giving advice but hopefully it'll help at least a little...