I think it would be good to at least tell her, clearly, that you are seeing other people, and to let her know there's no one serious -- that way she can know that you're being as straightforward with her as she's being with you. But since none of the others are serious, there's no reason to do introductions.
And yeah, after the first date may be too soon to meet her other bf's. I think if I felt like you do I'd tell her that I'd be open to meeting them someday if it's important to her, but that I want to are where things are going first.
DADT can work fine when things are casual, but it can really force someone to "compartmentalize" their life if things get serious. For instance, let's say she wants to have a birthday party but you still don't want to meet the other guys in her life. Does she insult them by not inviting them or by asking them to pretend they're just friends so as to cater to your feelings, does she tell you that you just can't come if you're not cool with it, or does she just avoid any situations like this?
Openness may feel uncomfortable at first, but ultimately it can make things way simpler and more chill for everyone involved.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.