There's no way to know for sure what the toll of a modern measles outbreak in the US would be. However, it seems the author of that article used only the facts that would support his case. The article he cites when coming to his conclusion is Measles Elimination in the United States.
First, the numbers he uses from 1956-1960:
Not all cases were reported to the public health system; from 1956 to 1960, an average of 542,000 cases were reported annually.By the late 1950s, even before the introduction of measles vaccine, measles-related deaths and case fatality rates in the United States had decreased markedly, presumably as a result of improvement in health care and nutrition. From 1956 to 1960, an average of 450 measles-related deaths were reported each year (∼1 death/ 1000 reported cases)...
So we have 450 deaths from 542,000 reported cases, or 0.83/1000. This is where the article gets the 450 number, claiming this represents the worst case scenario, since public health and medicine has gotten better.
However, it completely ignores a more recent outbreak pointed out in the same paper:
Nevertheless, a resurgence of measles occurred during 1989–1991, again demonstrating the serious medical burden of the disease. More than 55,000 cases, 123 deaths, and 11,000 hospitalizations were reported.
By the logic used, the death rate should have been lower after ~30 years, due to advances in medicine. Instead, we have 2.24/1000, not quite three times the rate in the late 50s.
Of course, these numbers could be a bit off, since they are using the number of reported cases, but it seems clear that the author found the one number that supported his point and didn't bother with the others (and just pulled 200 from nothing but an unfounded assumption).
As for bicycles, the number most often used is probably the 677/year, reported by the NHTSA for 2011:
A total of 677 pedalcyclists were killed in motor vehicle crashes in 2011.
However, I think it's important to note that as gerrit commented, that number is specifically for motor vehicle crashes. I can't find a number for how many deaths are caused by bicycles per year, but my assumption is that it's much lower.
It also ignores that far more people ride bicycles in the course of a year than contract measles (even before vaccines). The National Bicycle Dealers Association has this to say:
35.6 million Americans age seven and older were estimated to have ridden a bicycle six times or more in 2013, according to the National Sporting Goods Association. This number was down 9.4% from 2012 that had 39.3 million participants. The peak participation year was 1995, with 56.3 million participants. It should be noted that the age limit on this number eliminates millions of young people who ride bicycles with wheel sizes 19" and under. It also does not count those who rode a bicycle fewer than six times in the year.
Taking these numbers at face value, bicycles have a death rate of 0.02/1000, which is about 40 times lower than measles. While the true number of bicycle riders may be a bit above or below that estimate, the rate is nowhere close.
Of course, as mentioned in the comments, this is only the death rate. There are other complicating factors (20% hospitalization rate in 1989-1991, for example), which I believe makes this a false comparison at best.