I usually just hold my daughter until she says she is ready for me to let go when she starts crying over something when I'm around. Sometimes I even cry with her a little. Then, we talk about it.
To answer your question, "will she have to avoid serious literature for the rest of her life?" I'd agree with the other answer and say no. The key is choosing books your child is ready for, but still engage her with difficult themes (like death). As she matures, she will be ready for increasingly complex and difficult aspects of any given theme.
If you'd like to "prepare" her for reading "bridge to T" with her class, I could find some other books that are shorter with similar themes in a simpler format. You can use a subject access guide to find such books. This link will take you to one a posting about one I have used. They are reference books that allow you to look up children's and YA books based on subject/theme.
One of the things I told my daughter when we read the Little Match Girl, which has partially helped with other stories is that the cool thing about books is, if you want the character to live again, all you have to do is pick the story up and read it again. My daughter, likes the idea so much that even though she hates writing stories, she has started writing her own fan fiction-like stories where characters she loved (but "are no longer with us") magically come back and live again. Or where she changes the story and finds a way to create story bumps that don't kill people off. It really seems to help her a lot.
As Mary Jo mentions, you can pre-read the book together so she can process things with you first. This is a great idea because just having heard it once already can make the blow a lot softer the second time around. My daughter lost it sobbing and crying when Gollum realizes he has lost his ring in The Hobbit the first time we read it, it was no big deal, "I knew what was coming mom so It's all good" - of courses that was nearly two years later so it may have also just been maturation on her part too. The teacher may have objectives regarding "predicting" however, so teaming up with the teacher even at this point may be helpful in terms of making sure your daughter gets the most out of her experience with the book.
While there is nothing wrong with crying, or getting emotional over a particularly sad "scene," doing so during class might be embarassing or awkward for your child and difficult for her whole class. I wouldn't bring the possiblity up with her (because then you are planting a seed of doubt that may otherwise never have arisen), but if she expresses this fear (having thought of it on her own), respect it. Even if you've done a prior read-through, this may be an issue if there is to be any "in-class" reading and it still makes your child sad enough to cry more than a quiet tear or two. Kids can be cruel. I'd at least give the teacher a "head's up" just in case. Hopefully, when it comes time for Bridge to Terabithia, with the class, your daughter and you will feel she is ready, but if you don't you still have options:
If you feel your daughter simply isn't ready for the book yet. Approach the teacher with your concerns but keep your concerns focused on your child. You might offer up an "alternative" book reading as an idea. Simply ask the teacher if there are other novels that will still meet the reading objectives for the unit your daughter can do instead of "Bridge." If you read the book, but your daughter is worried about reading in class, have her do the assignments etc. but talk to the teacher about which portions of the book will be read in class and which will be read at home - your daughter can practice with the scenes marked as "in class" reading, or you can see if she can opt out using the excuse she already read the book anyway.
Good Luck to you and please let us know how it works out for your daughter.