I came out both as bi and as trans. (First as bi, and later as trans, 1-18 years later depending on the person). In my life, I have experienced much more rejection and biphobia when I outed myself as bi (or was outed) than rejection or transphobia for outing myself as trans. There's a couple of reasons for that:
1. My friends were already preselected as I had avoided anyone who was bi-, homo- or transphobic for decades. I got no problems from my friends.
2. I was not out as trans at work, but changed from a female mode work to a male mode freelancer job and none of my clients know I was not born male. Therefore, no trans coming-out trouble at work.
3. When you come out as bi, people tend to ask you many more stupid or extremely intimate questions than when you come out as trans, plus some of the questions can be very insulting. Being asked what you have in your pants and what you are planning to get there is absolutely harmless compared to the typical clueless bi questions (So you need threesomes? so you can't be monogameous? What are your sex practices when with males opposed to with females? When will you make your choice? But bisexuality does not exist? You must be very confused, don't you? So you're always in love with two people at the same time, one being female and the other male? etc.) And honestly, bisexuality is so common they should know a bit better. (Trans is so rare that I don't expect people to know much about it.)

4. At least here, when you come out as trans, people will rather talk behind your back than tell you directly what they think, opposed to a bi coming out. I don't know if it's better, but at least it spares you many stupid questions.
5. Often, people just don't believe you that you're bi when you tell them (which is very annoying). Whereas, after two years on testosterone and without a name change, you can prove them that you are trans if you really want to.
6. I had already gathered a lot of experience from my bi coming outs, which helps me figure out whom I can out myself as trans and where I better keep it to myself.
7. I guess bi is less accepted by society than gay. From the straights, you get both homophobia and biphobia added together. From the gays, you get biphobia or they just think you're a closet gay. Or, version nr. 2: it's just invisible, people will assume you're either gay or straight or they won't believe you if you tell them, which is a different kind of "not accepted". So the difference between coming out as bi and as trans is not as big as it sounds when it comes to acceptance by society.