Rapid Coming Out Process

Hey EC! First time poster, long time lurker. I want to thank everyone for the existence of this community as it has really helped me come to terms with my own sexuality and coming out process. I'm 22, 'bisexual' (although I prefer to say that I am attracted to both men and women at fluctuating intervals) and have only recently started to come out to my friends. The reason for doing this is because I've begun to date another guy for the first time a few weeks ago who lives in a nearby city. I came out to two of my best friends two weeks ago (both male, one of which is straight and the other is gay) and they took it extremely well and were supportive to the umpteenth degree. I felt happy, liberated and secure in knowing I can bring my date over to meet my friends. On Friday, I came out to another four friends at a party (albeit slightly intoxicated, which was fine) and, yet again, it couldn't have gone any better. I'm glad I no longer have to hide this side of myself (especially at the age of 22) and that I have the most supportive friends in the world.

I'm looking to come out to my parents and brother in the very near future as I don't want to hide the fact that I have a boyfriend. I know my parents are supportive of the LGBT community and my mom has asked me several times if I was gay based on my long-term single status. Although my mother has some misconceptions about gay/bisexual males (based on stereotypes that I do not fit) she does seem rather supportive and loving. My father is more similar to me in terms of our liberal views on almost every social issue. My brother is quite a few years younger than me and we don't hangout due to our age gap, so it would definitely make for an awkward conversation. Finally, my parents are European immigrants and I'm not quite sure that they could grasp the idea of me being bisexual. I'll probably have to say that I like both girls and guys to send a clear message. The problem is that I'm terrified to come out to them (more so than my friends) for petty reasons such as my lack of courage. Any advice as to how to get over this? Or the approach I should take to coming out to my parents, as opposed to coming out to my friends? My boyfriend encourages me to come out to my family as I won't have to 'hide' my relationship, to which I totally agree. It's just the approach I can't figure out as I'd like the conversation to be as casual as possible.

TL;DR: Have a boyfriend for the first time, already started coming out to my friends, looking for advice as to how to gain the courage and find an approach to come out to fairly liberal/accepting parents.

Some humour: this morning I accidently came out to my boss (who is female) by texting "Morning, handsome", which was obviously meant for my boyfriend. She 'LOL'd' and basically asked who the "lucky guy" was. Just goes to show how accepting everyone has been.