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Freezing leafy vegetables is difficult because the cell walls are broken by the ice crystals, degrading the texture. Even after blanching the bok choy you will still lose some of the freshness, and further cooking will lead to a mushy mess. If you plan to use it for something like soup where the texture is less important, this might be okay. 

If you cook the bok choy in a dish first you can avoid the need to cook it again, which will generally lead to better results. Stir fries would be an example, but it will still not be as good as fresh. 

You can also try making kimchi with bok choy. I really recommend this, as the fermentation process naturally preserves the vegetables and it's quite delicious!