Sounds like you are under a little deadline pressure. I have no personal experience with this experiment, but have just done some internet research with google. My conclusion is this experiment only works well by creating a vacuum in the bottle and sucking the egg in - it appears difficult to do by pushing the egg into the bottle by means other than a pressure difference.
1) using a glass rather than plastic bottle
2) having the bottle diameter be about two thirds the diameter of the egg
3) setting the egg on the bottle tapered side down
4) using vegetable oil to lubricate the bottle opening
5) one can create the pressure difference by heating the bottle either with very hot water (applied outside or inside) before placing the egg on the bottle neck, or
By placing the egg on the bottle and then placing the bottle in very cold water, or
By lighting a small fire in the bottle and placing the egg on the bottle neck.
One person claimed it was possible to place the vinegar softened egg and the bottle both submerged in water. The proceedure is then to roll the egg with your hands into a long tube that can be slipped into the bottle. This might be possible, but I think it is a real long shot.
The safest way is to use a shelled hard boiled egg placed on top of a bottle with the appropriate sized neck that has a small fire inside the bottle, with the pointed end of the egg down. This is almost certain to work.
You may get other formulas to work with some experimentation, but I cannot tell you with assurance how.
Here are the links to sites I found discussing the experiment: http://www.wikihow.com/Place-an-Egg-in-a-Beer-Bottlehttp://www.teachingk-8.com/archives/int ... owens.htmlhttp://www.everythingesl.net/lessons/eg ... iments.phphttp://bizarrelabs.com/egg.htmhttp://answers.yahoo.com/question/index ... 844AAVP7Dqhttp://www.elmhurst.edu/~chm/demos/egginbottle.htmhttp://www.knoxnews.com/news/2008/mar/1 ... he-lesson/http://chemistry.about.com/b/2008/02/12 ... ration.htmhttp://space.newscientist.com/article/m ... -word.htmlhttp://www.zianet.com/overkill/dopeland/eggtricks.htmhttp://video.aol.com/video-detail/egg-e ... /445355143http://www.cyberfriends.com/scripts/for ... number=283
Good luck with your science fair!