In principle the right to speedy trial applies to all federal defendants, and DC is under federal jurisdiction. But a speedy trial, while a good right to have, is a difficult one to exercise. IIUC, and IANAl, you have to exercise it in early proceedings, but in early proceedings the defendant is at a disadvantage because prosecutors have had ample time to prepare and they knew they were going to indict while the defendant did not, so the defendant has 71 days to prepare a defense while the prosecutors had no time limit in preparing their case. I suspect few defendants ever demand a speedy trial.
The right to a speedy trial may well have been incorporated against the States, but I don't know. In any case, a speedy trial mostly seems to mean that there must be a statutory limit to how much time can pass between indictment and the start of the trial, and between the start of a trial and closing arguments. Different States have different limits, and the variation in those limits surely must be constitutionally allowed, provided that in general they are a) statutory, b) not very long. I suspect a State could get away with 90 days from indictment.
EDIT: Defendants don't actually get to waive the right to a speedy trial, but if they don't assert that right, then they don't get to ask for dismissal of charges due to violations of the right to a speedy trial.
> The right to a speedy trial may well have been incorporated against the States,
The right to a speedy trial is incorporated against the states, yes. Klopfer v. North Carolina, 386 U.S. 213 (1967).
> a speedy trial mostly seems to mean that there must be a statutory limit to how much time can pass between indictment and the start of the trial
No, it doesn’t, nor does it provide such fixed limits on its own, instead being applied lookong at reasonableness case by case. The Speedy Trial Act of 1974 providing federal limits was largely a reaction to this, rather than required by it.
I was referring to the Sixth Amendment right to a speedy trial, since the amendment itself does not set such limits, the question is: what does "a speedy trial" mean? I've not looked at case law, but ISTM that having statutory limits and remedies must be a big component of what the right actually means.
The right to a speedy trial may well have been incorporated against the States, but I don't know. In any case, a speedy trial mostly seems to mean that there must be a statutory limit to how much time can pass between indictment and the start of the trial, and between the start of a trial and closing arguments. Different States have different limits, and the variation in those limits surely must be constitutionally allowed, provided that in general they are a) statutory, b) not very long. I suspect a State could get away with 90 days from indictment.
EDIT: Defendants don't actually get to waive the right to a speedy trial, but if they don't assert that right, then they don't get to ask for dismissal of charges due to violations of the right to a speedy trial.