Hmm I must have signed in officer.com by accident instead of Macrumors.com. This topic is something I know a good deal about actually, and not because I have received a bunch of tickets. I was a police officer prior to going to law school. The signature at the bottom of the citation is typically just an acknowledgment of receiving the citation, not an admission of culpability. The whole process is just an added measure to ensure notice is provided to the defendant that they will need to appear in court. Nevertheless, your signature is not required; how many criminals (I am specifically referring to criminals who get motor vehicle violations and know the system, not the average mac loving citizen who gets a ticket once and a while) do you think would actually sign it if they knew failing to do so would result in their citation being dismissed? I, and every police officer I know, write in the signature area "citation received" because people always want to get into it with you over why they will not sign the ticket and it is an officer safety issue of reaching in the car window and allowing someone to take a sharp metal pen.
Unless you really are seeking a way to get out of this specific ticket and are confident that a citation lacking a signature is dispositive of liability, I would suggest you find a way to sign the ticket. While I highly doubt anything would happen to you if you simply said you are too busy and that she should have asked you to sign it when you were stopped, the concern I have is less the immediate one ticket issue and more the fact that you will now have a pissed off cop in front of the judge looking for any reason to screw you on the ticket process. Look, most cops are pretty decent people and some are actually really cool and badass, but some get power trips and it would suck if you got the latter.
In the end going to sign the ticket, being cool and nice to her if she seems at all receptive, might result in something you don't expect. If she is on you to sign this, then there is likely some reason she cares. I would suggest that when you meet up with her you be nice and say look I took time off from work to come here, this ticket is really going to kill me, how many people do you know that would come down here... is there anyway you could help me out a little by reducing the speed (if it was high enough that this would help) or making one of these a lesser infraction or something, I would really appreciate it, especially in light of the effort I made to take care of the signature issue.
Good luck! and let me know how it goes.
Two qualifying points
1. I was a police officer in a very large 500+ officer police department so I have seen my fair share of you know what during my time on the job.
2. I sure as heck was not a Virgina police officer so there is clearly a chance they have different motor vehicle codes that require your signature, but it is unlikely.