Could I submit an abstract for a conference prior asking my supervisor permission about it? I would like to submit an abstract for a poster presentation, I'm just worried that if I tell my supervisor before submitting, she might say I shouldn't do it, because she rarely wants me to be away from the office. So I was thinking on submitting the abstract and once I'm accepted telling her I've been selected for presenting at that conference. What do you think about it? Would this be a good strategy for attending a conference when having a strict and closed minded supervisor?

P.S. Our research is not about any kind of product or patent we're developing for a company, so no privacy issues apply in there.
Yes you could.

I'd strongly suggest you not do it.

Your supervisor has a lot of power over you - they aren't someone you want to upset.

It is unfortunate that your supervisor is not supportive of you trying to seek out conferences to present at, but you should address that issue with them rather than try to go behind their back. I would suggest trying to find another supervisor before I would suggest trying to undermine the authority of your current supervisor: there just aren't enough positives for you on that path.

Note that if your supervisor deserves authorship on your work, either omitting their name as an author or submitting without the approval of someone listed as an author could be considered academic misconduct. In some fields, authorship by only a student without their supervisor is common, but if you aren't in one of those fields you should be especially careful.