FWIW, I subclassed the mmPicker and made a get property that returns the ControlBindingsCollection of the text box in the mmPicker control. Not happy with the property name, but whatever.

using System.Windows.Forms;

using OakLeaf.MM.Main.Windows.Forms;

namespace Adc.Windows.Forms.Controls
{
	/// <summary>
	/// Summary description for AdcPicker.
	/// </summary>
	public class AdcPicker : mmPicker
	{
		public AdcPicker() : base()
		{
			//
			// TODO: Add constructor logic here
			//
		}

		// Can't just override DataBindings, so need a new name.
		public ControlBindingsCollection DataBindings2
		{
			get {return this.txtEntry.DataBindings;}
		}
	}
}

So now I can do this in code

this.pckHowReceived.DataBindings2[0].BindingManagerBase.Position = howReceivedPosition;