There are new Bezier Tools improvements implemented during Google Summer of Code 2016 that do exactly what I wanted in my original question from 2015:
https://wiki.blender.org/index.php/User:Genio84/gsoc2016/final_report/
Offset tool
The Offset tool allows you to offset the selected spline. Due to the
mathematical details of Bezier curves, true mathematical curve offset
(i. e. where the distance between every point in the curve and its
offset is equal) is not possible. This tool offers an approximation
based on the algorithm. Offset distance can be
inputted in three different ways (mouse, keyboard and tool shelf).
The offset tool will add a new spline where each control point is at a fixed distance from the original one. It is not possible to offset line segments.
To use this feature however, you will have to wait for the release version containing it, compile Blender with aforementioned patch yourself or download a test build from GraphicAll:
http://graphicall.org/1194
You will find "Offfset" option in the "Modeling" section, or press Shift + O while in Edit Mode:
