How to approach casting directors about submitting your showreel
Well firstly I would say that a showreel should be online rather than on a C.D or DVD. By all means have a physical copy stored away in case someone specifically asks for one, but these days casting directors work so heavily online that your showreel needs to be there where it is easily accessible. Ask yourself, if you were in a busy office and you had the choice between, A) clicking a link on the computer to watch a showreel, or B) finding a DVD, getting it out of the case, sticking it in your computer, waiting for it to load up and finally watching it, what would you choose?
This influences the answer to the question, because if your showreel is online you don't need to approach casting directors about submitting your showreel, you can just submit it.
If you have no other reason to write (i.e you're not applying for a specific job) then it is totally fine to send a brief e-mail telling the casting directors that you have a new showreel and asking that if they get a spare three minutes would they please take a look at it. If it's short (about 3 mins) I think this is worth mentioning too. Include a link to the showreel and you're done. What you musn't do though is keep sending e-mails afterwards checking if it's been watched as you will annoy them. Send it once; you can send it again after 12 months if it's been updated.
Most casting directors that I have spoken to have actively encouraged actors to get in touch when they have something useful to say, (new showreel, currently appearing in such and such, applying for a suitable job etc) so if you have a new showreel get in touch, it's a perfectly valid reason.
And keep an eye on Twitter, as a few of the newer casting directors have offered to watch showreels and give feedback.