Personally no, but then that is me and my specific opinions on things like sex and relationships are quite different to some other people's. I would be interested in trying an open/polyamorous relationship if I trusted the person I was with, and also knew that they completely trusted me.
It sounds like you think it wouldn't be something she would be into. If you know she would be more comfortable in a secure monogomous relationship, I don't think you should ask.
The fact that it's a long distance relationship may make it being open more difficult for her, if she is used to you two being together with only eachother. I would imagine it would be far easier to get jealous or insecure if you can't see the person you are with every day.
Perhaps try an indirect way of bringing it up, rather than outright asking her to do it (which, if she is not interested, could really undermine her trust in you), simply ask her opinion on that sort of relationship, or ask if she ever felt like she wanted to sleep with someone else.
Another thing to consider is the practicality of finding other people to sleep with or whatever it is you want to do, without hurting them or leading them on. For some people, if you told them you had a girlfriend, they wouldn't feel comfortable doing anything with you. Or, they might think you are really wanting to end your relationship with her and start a new one. If you don't tell them, you risk leading them on - they could end up thinking you want to be in a relationship with them.
Whatever you decide, I'd advise you to go carefully and slowly. Consider whether you're doing this because you think it's the right thing for both of you, or just because you are bored or lonely.