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I'm sorry that Bear is such a fearful dog.  It's sometimes impossible to totally overcome early lack of socialization.  You don't know what Bear's background is but it was obviously not one that introduced her to the world in a positive way. 

 When I have a puppy, I never let them spend too much time with my other dogs.  Not because I'm worried they will pick up bad habits but because I want them to focus on me and not become too dog oriented during the crucial socialization period.  That doesn't mean they are isolated and never allowed around my dogs or other friendly dogs.  I hope you find a good puppy class for your new pup.  Socialize, socialize, socialize for the first 16 weeks.  If you are worried about contagious diseases, before all the shots are completed, carry the pup in your arms.  Rides in the car and parking in different areas with the windows down introduces sights, sounds and smells.  Sitting on a bench outside a store and holding the pup allows him to see lots of new people.  I always erred on the side of risking a disease rather than having a dog who was fearful due to lack of socialization.  I've seen too many dogs live very limited lives or lose their lives due to lack of socialization. 

Don't feel guilty about getting a dog that will be what you want.  I have three dogs and each is unique and requires my attention in different ways and at different times.   Good luck with your new puppy. 

edited to change Bear from a boy back to a girl dog. :)

 Buy a copy of "The Cautious Canine" and try some of the techniques to help Bear.  Don't fret so much about the puppy - do as Jackie suggests and take it to puppy class.  Many positive trainers let pups in to their kindergarten classes very young (my own dog went at 10 weeks of age).  If you start out socializing the puppy to many different pups and dogs, and do obedience training from such a young age, the likelihood is greater that the pup will bond nicely with you.  Instead of assuming that Bear will get less attention, don't be selfish or overindulgent of the pup - PLAN to give Bear some attention and training without puppy around.  You shouldn't have to care if Bear can't go in the car.  That will be the pup's thing.  But, there's no reason you can't devote some time to Bear, too, and if you can't you have no business getting a puppy just to fill your own needs - you took Bear in and are responsible for her welfare.  That's what responsible adulthood is all about.

 If you tried to introduce Bear to adult dogs in the past, but not puppies, she may accept a pup better, although that isn't a given.  Older dogs usually tolerate very young puppies.  However, there are also some dogs that bully puppies, so you should probably be prepared either way.  I can understand you getting a bit defensive at our comments, but you made the comments you made about Bear, and we don't know you all that well.  Suffice to say that, from your own words, we were worried.  But, I'm glad you are committed to Bear.  Her life can't always be easy, and she deserves what peace she can have.

 Well, I guess I should have paid more attention to your original post - it said you weren't looking for an answer.  That is abundantly clear, because had you asked, I guess my question would have been why do you even have to get a puppy now?  If it's going to cause all that chaos, why do it?    Sorry to have offended you, but it is an Internet forum, and if you are going to rant or vent, you have to suppose that others might answer, and not always in ways you expect. 

This was a useless post, so I erased it to keep anyone else from wasting their time.