Most of what will be readily available in English is going to be contained in more general overviews of Burmese history. That's not to say they don't get into reasonable detail though.

• Andaya's A History of Early Modern Southeast Asia, 1400–1830 is a good overview that addresses Taungu in the context of SE Asia more generally

Then there are a number of reasonable gneral histories which spend time on Taungu:

• Htin Aung's History of Burma

• Harvey's History of Burma

• Topich & Leitich's History of Myanmar

• Aung-Thwin's A History of Myanmar Since Ancient Times

Bayinnaung is still revered today, and has no shortage of text about him written in Burmese. However I'm not sure of anything devoted to him in English.

There's a Civ VI mod too where you can play as Bayinnaung, which I obviously wouldn't suggest as a historical source, but it's worth downloading if you play Civ VI, because Bayinnaung.

Is there specific stuff you are looking for, or just more general interest?

edit: see u/PangeranDipanagara's comment for what I've missed.

I agree with /u/Keyilan's post generally, but he misses the only real English-language work that focuses on the history of Taungu Burma (and which, by virtue of not only its uniqueness but by being an excellent work of scholarship in general, is really the English source to consult for the era). That work is Victor Lieberman's Burmese Administrative Cycles: Anarchy and Conquest, c. 1580-1760, which, despite its subtitle, does spend a lot of time on the First Empire.