I think what she knows when she sees that Beaver was on the team, is not that he blew it up (though obviously she suspects him), but rather that he raped her.
She had chlamydia, but doesn’t know how she got it. She and Duncan apparently used condoms (not that they’re foolproof, but they cut down on the risk of transmission), and that’s the only guy (as far as she knows) that she’s been with. And as far as she can figure out, Duncan was only with Meg, who was also a virign when they slept together. So something doesn’t add up there. She knows someone must be lying or something that she thinks she knows just isn’t so, but she doesn’t know what. So then she hears that Woody was treated for the same disease, which gives her a little shock, but still, she has no reason to think that’s anything other than coincidence.
Then she sees that Beaver was on the team. Woody had chlamydia. Woody abused two boys on the team that she knows of, and could have abused Beaver, thus passing along the disease to him. And she was alone with Beaver, drugged and unconcious, at the party two years ago. She had previously believed his denials that anything happened, but now she has to reconsider that. This is the most plausable scenerio she’s been able to figure out for how she got chlamydia. It’s not 100% absolute proof, sure, but Veronica has been known to come up with a plausible theory before and treat it as the proven truth (like in last year’s finale when she thought Logan killed Lilly based upon him lying about his alibi).
So, next scene we see her in the bathroom, looking freaked. Because now she figures she was raped after all, and if Beaver could do that to her and keep that secret for so long while being friendly to her and pretending nothing happened, what else is he capable of? We don’t know how long she was in there, but it could have been several minutes. She’s probably running through bunches of scenerios in her mind, trying to figure out what happened. She comes out of the fast food place and calls Mac, leaving a message that Beaver is dangerious, because, even if she’s not completely sure at this point that he’s the killer, I think she’s convinced that Beaver did rape her, and that certainly makes him dangerious. Then she starts digging into Beaver’s past by calling his friend Hart (on that point, I’m not sure quite sure what made her think of him) and assembling a more complete picture of what happened.
It, more or less, works for me. YMMV. I do think it suffers a bit the first time someone sees the episode though. When I saw it, I too thought “wait, how did she leap from ‘Beaver was on the team’ to ‘Beaver is the killer’?”. It seemed like too large a leap absent other clues. But there was another clue, which was that Beaver raped her, which we didn’t know yet (well, it was possible to figure out since we knew as much as Veronica, but it didn’t even occur to me at that point). So, in that light, it works much better for me.