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 ...