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I put together some code to find least-squares approximations for a few formulae using the NA refraction tables as the inputs.  Refraction is in arcminutes and altitudes in degrees.

Bradley's model:

r = 0.92 * cot(h + r * 2.86)

• Errors for (fomula - table) range from 0.5' to -1.0'
• The model says this should be the same thing as r = cot(h+ r * 2.63)
• If 2.86 * r is small and r² is approximately 0, this all reduces to r = 0.92 * cot(h)
  • The 0.92's start to differ with the third decimal place.

1/h model:

h = 81 / (h + 2.3) -1.1'

• Errors for (formula - table) range from 0.9' to -0.4'
• If you want to use this as a "first guess" in the Bradley model, r = cot[ h + 3.6/(h+2.3) - 0.05]
  • You can probably drop the 0.05 at the end.