Bullets in the American West cost about 2 cents a round in 1890.

That's not extremely expensive.

The centerfire 44-40 cartridge was probably the most popular ammunition in the Western US in the 1880s, as it was used in both the 1873 Winchester rifle and the Colt "Frontier" revolver.

As per the Colt catalogue of 1890, as quoted in this post:

http://thefiringline.com/forums/archive/index.php?t-480020.html

the price for 1000 rounds was $19.45 (presumably plus postage).

That's about 2 cents a round.

A top cow hand made $25-$30 a month plus "found" (room and board).

Here are some prices for goods in the West from the 1870s:

1 good saddle horse - $200

1 good quality "cowboy" style saddle - $60

1 good quality custom made pair of "cowboy" style boots - $15 - 23

1 Stetson made "Boss" hat - $5

1 good quality revolver - $17-20

1 Winchester lever action rifle - $40

Cigars - 5-10 cents each

One shot of decent whiskey in a saloon - 50 cents

One gallon of whiskey bought in bulk - $2- 3

(There is a story that cowboys used to trade one shot of whiskey for one round of ammo, leading to the origin of the word "shot" for a drink measure of whiskey. This would not have worked well if whiskey was at a saloon at 50 cents a shot, but if buying whiskey by the gallon, a shot and a round of ammo would have been roughly equivalent value.)

All those prices from this source:

http://www.theroadtodeadwood.com/forum/index.php?topic=3331.0;wap2

Which has many more prices as well for goods and services on the western frontier in the 1870s.

Judging by this website:

http://www.ammunitiontogo.com/index.php/cName/rifle-ammo-4440

you can get this same ammo today at a price of about $0.74 per round.

I don't think that the price of ammo has dropped significantly. It has gone up from 2 cents to 74 cents in the last 125 years. If the price of bullets had gone up by the average rate of inflation between 1890 and 2016, they should cost 52 cents a round, but they seem to have increased by more than the rate of inflation.

It is not that the price of bullets has dropped, but it may be that the affordability of bullets has increased as incomes have increased faster than prices.

I would just like to add that 44-40 is nowhere's close to the most popular bullet today, which has a big impact on its high price. I don't know if you would want to compare the most popular bullet then to the most popular bullet now but both 5.56x45 (for rifles) and 9mm (for handguns) can be found for at or under 20 cents per bullet.