I would definitely say that bloodroot is
desirable. Although the flowers tend to be short-lived, only
lasting a day or so, more flowers follow for about 2-3
weeks. Their foliage is very pretty and it sticks around a
little later than most spring ephermerals. Bloodroots like
deciduous shade, with full or part sun in spring and
subsequent summer shade cast by trees and shrubs. They also
like a moist, woodsy soil, on the acidic side.

Bloodroot can be propagated from seed. But
you have to watch the seed pods carefully--they spring open
and shoot the seeds everywhere. You might try tying a piece
of cheesecloth over the ripening seed pod. To germinate them
see Harry R. Phillips "Growing and Propagating Wildflowers".

It can also be divided since it grows
from rhizomes. It is slow to establish, but it will form
eventually a large clump (1-2 feet across).

Another answer:

Bloodroot can be propagated both by seed
and division. You can rely on self sowing which is aided by
ants which carry the seeds off. (I have some growing out of
my stone wall.) Or you can just scatter the seed in either
prepared beds or among the leaves and debris on your forest
floor. Although individual flowers last only a few days, if
you have some growing from sunny spots to deep shade, you
can get three to four weeks of bloom. In 30 years my three
plants or so have multiplied to at least three thousand and
I have probably given away at least that many.
Even nicer than the type is Sanguinaria canadensis
flora-plena, a double form which looks like a small white
peony. It is sterile so the flowers last a week or longer.
Both the single and double can be easily divided either
spring, summer or fall by simply breaking the rhizome being
sure that each piece has at least one eye. I believe that
they should be dug up, divided and replanted on a regular
basis or they will go into a decline.