Help getting the right headset bearings
First you have to identify the type of headset. As you said its a external cup headset, but threaded or threadless?
Measuring the outer diameter of the steerer and the inside diameter of the head tube are also a good starting point. But try to measure as acurate as possible. +/- 0.1 mm - 28.6 mm (1 1/8&quot;) is pretty standard on the steerer nowadays, so 29 mm seems to be a weird or wrong value.
Replacing only the bearings would be a headache to figure out.
Manufacturers have a standard description of headsets called SHIS (Standardized Headset Identification System).
This park tools page should help you a lot to identify the required headset.
You have to figure out the measurements and fit the code together like in the example of the page: ZS44/28.6 | ZS44/30 - you can easily search for this code and find the fitting headset.
Good Luck.