One Dyson sphere of radius 1 AU (Sun-Earth distance) having mass 600 kg/m^2 (8-20 cm thick) will require[1] 10^26 kg of material. The Milky Way's dark mater halo is considered[2] to have mass 10^12 M_Sun = 10^42 kg. So you will need a total of 10^16 (10 quadrillion) spheres.
True. I only considered the spheres (shells) themselves. If you include the star then the result is even simpler. M_Sun is 10^30 kg so for a back of the envelope calculation you don't even have to consider the shell. Therefore you can say 10^12.
[1]: https://www.aleph.se/Nada/dysonFAQ.html#ENOUGH
[2]: https://arxiv.org/abs/1306.4013