I think what she's trying to avoid is being identified as part of a group about whom there is a view about what they are that she doesn't feel comfortable having assigned to her. Saying "I'm attracted to both gals and guys" is a statement purely about the individual's preferences, saying "I'm bisexual" identifies you with others who call themselves that. You can't necessarily stop someone conflating the two sentences, but you can try and get yourself separated from the group, if you don't want them to immediately jump to whatever society's idea of that group is.
I probably wouldn't do it, personally, because I find it useful to use these labels. I have no problem calling myself a nerd, but I wouldn't fault someone for wanting to distinguish themselves from the group:nerd if they didn't feel society's idea of group:nerd defined them in a useful way.
Edit: Is the Tedd situation different? To me it does seem like one of the best examples in the comic of both sides of an issue having a proponent (Tedd: labels = good because I can identify with a group, Ashley: labels = bad because I don't want to) with Ellen being in the middle of the spectrum.