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With a well established bed, I would not worry about leaving all the female Asparagus.

These links have more information.

https://www.gardeningknowhow.com/edible/vegetables/asparagus/male-female-asparagus-plants.htm
https://www.gardeningknowhow.com/edible/vegetables/asparagus/harvesting-asparagus.htm

They will not reseed, as males cannot produce seeds. They only produce pollen. They will still reproduce with their roots, though. They will spread in that way, rather than spreading by seed. Also, these will all be male, since they are just extensions of the same plant.

This article will help you with the care of asparagus: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm

According to the University of California, asparagus berries (and presumably their seeds) are poisonous and should not be eaten.

http://ucanr.edu/sites/mgslo/newsletters/Poisonous_Plants28032.htm

You could leave in the greenhouse and plant out in spring. They need to have a cold period and you should add extra insulation around them.
Make sure they do not completely dry out.
https://www.gardeningknowhow.com/edible/vegetables/asparagus/propagating-asparagus-plants.htm

This article will get you started with growing asparagus: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm

Some people do prefer to cut it back, but this is not advised. It will slow the next years growth. Here is an article that will help: https://www.gardeningknowhow.com/edible/vegetables/asparagus/growing-asparagus.htm