New Glen is their orbital rocket but it is not ready yet. Hopefully it will be ready for some of the launches, but it must hurt owning a rocket company and having to use another companies to launch your satellites.
From the project web page
"Project Kuiper has secured 80 launches from Arianespace, Blue Origin, SpaceX, and United Launch Alliance, and we have options for additional launches with Blue Origin, providing enough capacity to deploy the majority of our satellite constellation. The agreements comprise the largest commercial procurement of launch capacity in history, and support thousands of suppliers and highly skilled jobs across the U.S. and Europe."
It's worth mentioning too that BO is following the same strategy as SpaceX (and others), in becoming their own customers. Lesson learned from the 90's launch vehicle boom. Companies couldn't scale without customers, it's a vicious feedback loop. No customers because prices are too high, can't bring prices down without more customers. Either you have to become your own customer or you have to bootstrap. It's a long way to bootstrap and an expensive industry.
Though using ULA is kinda a bridge to the looking deadline[0]. So if they can't get satellites up now they won't have this means for being their own customer in the future.
They need to launch fast with as many launchers as they can, due to their looming FCC deadline. The more they launch, the better their odds for getting an extension to their deadline as more launches demonstrates their seriousness.
They're even going to launch on Falcon 9 (albeit after a shareholder lawsuit..)
Did shareholders not want them launching on a Falcon 9 because it was helping a competitor, or did they actively want them to use the F9 because it's the most affordable option but Bezos (or other higher ups) didn't want to support a competitor?
The latter. SpaceX isn't an Amazon competitor if Amazon doesn't have their constellation in the first place, and the loss of a handful of launch contracts from Amazon isn't going to slow SpaceX down (while on the other hand, it would slow Amazon down considerably.)
Bezos didn't want to launch with SpaceX because SpaceX is a Blue Origin competitor. Shareholders sued over this, saying that Amazon was putting Bezos' personal interests before Amazon's own.
New Shepard has limited payload delivery capacity. It's mostly for crew and experiments held in lockers in the crew compartment.
New Glenn has a 100,000lb to LEO payload capacity which makes it absurdly oversized for this mission.
Atlas V has a 18,000 to 42,000lb to LEO payload capacity. The variable solid rocket booster configuration really gives this platform the most flexibility for customer needs.
You are suggesting that they should design a brand new upper stage to get the thing to put 50 kg into orbit, as an alternative launch platform for their 600 kg satellite? Instead of investing that engineering effort into finishing their New Glenn rocket which delivers 40,000 - 100,000 kg at a time to LEO?
From the project web page
"Project Kuiper has secured 80 launches from Arianespace, Blue Origin, SpaceX, and United Launch Alliance, and we have options for additional launches with Blue Origin, providing enough capacity to deploy the majority of our satellite constellation. The agreements comprise the largest commercial procurement of launch capacity in history, and support thousands of suppliers and highly skilled jobs across the U.S. and Europe."