Blue is the hardest colour to maintain. And doing it on your own (especially if your don't use bleach often) is a total and complete pain in the ass, and it most likely will not turn out. Hair has to be bleached to almost white to take the colour properly. Any hint of yellow, and it will turn a weird green colour. Once the dye starts to wash out (and it will) your hair will get more and more greenish coloured, just like how white blondes turn yellowish over time if they do not use special shampoos.
There are things you can do to prevent the colour turning, like using, or mixing a coloured conditioner, or avoiding any and all products with sulfates it in, washing your hair less frequently always helps too.
Once a stylist has done the initial placement, bleaching and colouring you can always keep up the colour yourself. You can either use a vegetable based dye (special effect, punky color, manic panic) which is a thick gel/cream consistency that require no mixing (these wash out the fastest, but do not damage the hair), you can use a dye like joico or schwarrzkopf, or if you want to commit to blue for the long haul (and i mean like cut it out hault) you can go with illumen (sp?), which you will NEED to do in a salon. If you use one of the first two options, you can simply go back to see your stylist every few months to rebleach the root and maybe do a touch up if you please. Because they were peek a boos, regrowth will hardly show.
good luck.