according to nookipedia, blue roses are the result of hybridizing two 1110 hybrid red roses, which are produced by cross-breeding a yellow rose with a 1011 hybrid pink flower.
You can get a 1011 hybrid pink rose from cross-breeding a store-bought red rose (2001) and a purple rose. There is also a chance that you get a 1011 hybrid pink rose from breeding store-bought red and white roses.
Here is the chart from Nookipedia:
It's not clear to me whether this is accurate, however - I have successfully bred each of these necessary roses, and so far none of the 1110 hybrid red roses have produced a blue rose ... They have produced more black, white, and red roses, however.
Maybe it's just a matter of time, since the blue rose is a 1.56% chance ...
About 2 years ago my wife was able to get blue roses in about 60 days, it was Northern Hemisphere during the snow season. We tried using the same method at the same time in the Southern Hemisphere (summer) but did not do as good and finally gave up. She was extra careful to make sure she did not mix flowers, kept them well isolated. She did not allow them together until step 4, then she kept all the step 4 hybrid red roses together. It took up a lot of room isolating each pair to make sure they did not cross bred with the wrong flower. Each step she planted a new seed flower. We had flowers everywhere, every time we got a hybrid we moved it to a different spot and planted a seed flower next to it. If the pair produced anything other than the desired hybrid flower, it was trashed so not to get them mixed.
I pretty sure this is the method she used:
Step 1 : Seed White + Seed White = Purple
Step 2 : Purple from Step 1 + Seed Red = Pink
Step 3 : Pink from previous step + Seed Yellow = Hybrid Red
Step 4 : Hybrid Red from previous step + Hybrid Red from previous step = blue