The best methodology for preserving samples may depend on the toxins you are interested in, but for persistent organic pollutants (POPs) it is sufficient to keep the samples cool in the field and then freeze them at -20°C until analyses.
My grad student took the various organs of birds he was testing (fresh-killed or frozen) and placed them in vials and dried them at 60 deg C for 48 hours. Then he ground and homogenized them using a mortar and pestle. He then place ~ 0.07 g of each homogenized sample into 50 ml flasks into which 4 ml of nitric acid (70%) was added (adapted from Burger and Gochfeld 1990; McFarland et al. 2002)
Burger J, Gochfeld M (1990) Tissue-levels of lead in experimentally exposed Herring Gull (larus-argentatus) chicks. Journal of Toxicology and Environmental Health, 29(2), 219-233.
McFarland C, Bendell-Young L, Guglielmo C, Williams T (2002) Kidney, liver and bone cadmium content in the Western Sandpiper in relation to migration. Journal of Environmental Monitoring, 4(5), 791-795. doi:10.1039/b206045k
Maybe you can also use the feathers, that's maybe more easy?
Concentrations in bird feathers reflect regional contamination with organic pollutants
Jaspers et al, 2009, Science of the Total Environment, 2009
and
Eulaers et al, 2011. A first evaluation of the usefulness of feathers of nestling predatory birds for non-destructive biomonitoring of persistent organic pollutants. Environment International. Volume 37, Issue 3, April 2011, Pages 622–630
Perhaps you can store the bool on whatman paper. This holds the blood entirely and is very convenient in the field. The blood is easily retrieved in the laboratory.