When I have measured BSA in water, I use 5% w/v. One reason is that is what other researchers have used. Another reason is it has to be high because the protein molecules are small and scatter weakly. I'm not sure what you mean by a single run - it will require the same concentration no matter how many runs.
As a guideline, make sure you can see through the solution and that - if you have one - you can see the well-defined beam from a laser pointer shining through your solution.
I detected signal in solutions of mili molar range, 10 x diluted.
The dilution process is important to avoid the micrometer particles who can hide the signal of the small particles in your system. Another thing you have to consider is try to have an homogenous and stable solutions.
Broadly speaking, the answer is "it depends", but similarly to John, my starting point if I were to prepare a protein sample for DLS would be 5 mg/ml, prepared in a buffer filtered to 20nm.
The concentration limit for a DLS measurement of a protein is limited at the lower end due to signal to noise and the amplitude of scattering over the background dispersant, and at the upper end by the onset of particle particle interactions, or eventually multiple scattering. At high protein concentrations particle particle interactions tend come into place before before multiple scattering due to the low scattering nature that John mentioned, and will still allow a size measurement to be performed, however the size will typically be smaller than the expected hydrodynamic size at infinite dilution.
The specification typically referred to for minimum concentration for DLS measurements of proteins is 0.1mg/ml and this is based on lysozyme (Mw = 14.4 kDa). A larger, higher molecular weight protein may be successfully measured at a lower concentration.
This spec point is held by many commercial instruments, however performing a measurement at this low a concentration may not be trivial and may require some specific settings, such as extended measurement duration, and may be more easily carried out in a higher quality cuvette (quartz rather than plastic disposable).
The other challenge as alluded to by Juliane Pelin is sample cleanliness, as small, low scattering monomers of protein can be easily out scattered by larger aggregates or contaminants.
When performing stability screening measurements and a concentration ladder is used, the concentrations measured typically range from 1/2 - 10 mg/ml.
In terms of a "single run", would you please mind clarifying. Across different commercial instruments the terms "run" and "sub run" are both often used, sometimes interchangeably, to mean a single measurement or part of a measurement.