Caution, the following contains physics and will upset many pilots.
To calculate angle of bank for a rate one turn,
angle of bank = arctan( ( 2 x pi x TAS) / ( 9.81m/s^2 x 2 min) )
Be careful with your units (1 knot = 0.51444m/s).
Use TAS/10 + 7 and compare the two equations in Excel, you'll find less than 5% relative error between 120 to 180 kts and 340 to 590 kts (I did increments of 10 kts). Less than 10% relative error between 110 and 550 kts.
In the end, I'd say this is one of the better approximations we use.
Matthew.