BPO stuck in a bashed station

Will a blueprints being researched during bash go to asset safety?

Yes, at least that use to be the case. It is not mentioned on the current version support page, but you can see the discussion around this in this old thread:

https://forums-archive.eveonline.com/topic/515708/

They will go into asset safety unless the structure is abandoned or in wormhole space. If abandoned, the research will be stopped since the lab needs fuel. In this case you should be able to cancel the job(s) and manually place any assets you have in the structure into asset safety.

I don’t think it’s doable when the structure is being bashed. Need to check that.