Typically, the gray primers are used when you want to put a dark-colored top coat. You are doing the reverse.
Personally, what I would do is buy white primer, then cover the blue, let it dry, then primer the entire room. You might be okay if you don't primer the whole room, but I almsot always prime walls prior to painting.
Latex primers dry very quickly - and I think you can recoat most in a hour. I would think you could use a regular primer, but I would use a stain-blocking primer just to make sure the blue is sealed in.

You'll want to prime anyway if you want to do it right. You don't know what has been on that wall. Any greasy finger prints, whatever, can mar your new finish and cause it to not adhere properly. Primer is not only to cover up the color, but to provide a clean, fresh surface for your paint.

You want a primer, light grey or white, followed by two coats of paint.

Allow ample time for your coats to dry or you will end up removing the first coat when you go to put the second one on.

Wow - Thanks for the info! Painting has always confused me. What kind of paint is better to use? Latex, Gloss, Flat, etc? Its for a bedroom and i'm wanting to use the same paint for a bathroom.

There is a chance that there may be a ridge line where the blue paint meets the white paint. Add primer over top of the blue paint and you may make the ridge more noticeable after you paint the entire room pink, soooo.........before you are ready to paint the pink you may want to consider quickly sanding just the edge where you have primed where it meets the white to get a nice uniform finish of pink.

Did I make sense?

The advice on using primer is right on the money. As for type of paint, for interiors, latex is standard, but it's the finish (flat, eggshell, semi-gloss, etc.) that makes the difference. I find that an satin or eggshell finish works best in bedrooms. It's much easier to clean than flat paint (which is a plus in a kid's room), but it's not nearly as shiny as a semi-gloss or gloss. Semi-gloss is usually recommended for bathrooms because it stands up better to moisture and is easier to clean than a satin or eggshell finish.

Hope this helps!