Hi Cathy. I would definitely do sequential digestion, but you do not need to clean up in between. look at the composition of both buffers:
NEB buffer 2: 50 mM NaCl, 10 mM Tris-HCl, 10 mM MgCl2,1 mM DTT, pH 7.9
NEB BamHI buffer:150 mM NaCl, 10 mM Tris-HCl, 10 mM MgCl2,1 mM DTT, pH 7.9
What you need to do is to set up the Hind III digestion first, incubate for several hours, and then add enough NaCl to the digestion so as to increase the 50 mM NaCl in the buffer NEB2 to 150 mM final NaCL, and voilą, you've got NEB BamHI buffer! Then you only need to add BamHI and incubate for a further several hours. Done. Be sure to use an NaCL stock solution enough concentrated such as not to dilute much the other components in the digestion. For instance, if you digestion volume is 50 ul, you'd only need to add 1 ul of NaCl 5M, so it will not significantly affect the concentrations of the other reagents in the mix. I do this all the time when I do sequential digestion, I always made sure that I do first the digestion with the lower salt content in the buffer. It works fine, and you don't loose time dyalizing or precipitating the sample.
Also, I never bother in adding BSA, even for the RES which supposedly need it, but according to the NEB catalog, BSA would never hurt, so if you want to add it, you can add it already to the first digestion.
You can also check this previous thread:
http://www.protocol-...pic=4961&hl=bam
Hope that it helps! Cheers