You can either do a sequential extraction (see my paper Duarte et al., 2008) a overlook the first fractions (available and carbonate) or you can make an extraction using DTPA (see my paper Duarte et al., 2013 Functional Plant Biology). Both give informations about the metal bioavailability although in different ways. DTPA extraction is more accepted as a bioavailable measure.

It depends on what you mean by bioavailable. If it is bioavailable to human ingestion the Unified BARGE method is probably a good method. See Denys S, Caboche J, Tack K, Rychen G, Wragg J, Cave M, et al. In Vivo Validation of the Unified BARGE Method to Assess the Bioaccessibility of Arsenic, Antimony, Cadmium, and Lead in Soils. Environmental Science & Technology 2012; 46: 6252-6260.

DTPA method by LINDSAY &. NORWELL (1978) and Mehlich-3 method work wery well.

If your bioavailable Cr means extractible Cr, then Cr may be extracted from soil with 5 ml of the mixture (conc. HNO3 + conc. HClO4 in the ratio 2:1) with 5 ml of conc. H2SO4). Its concentration in the soil extract can then be read using AAS with Cr cathode lamp fixed. This method had been used for Pb. You may see 'Yield and quality of maize from spent engine oil contaminated soils amended with compost under screenhouse conditions' in Journal of Agrobiology 2013; 30 (1): 9-19.

DTPA by Lindsay & Norwell Is used mainly for extractable heavy metals portion in alkaline soils (calcareous soil). This extractable portion is representing the bio available forms of metal in soil. several studies indicated that the concentration of heavy metals in plant tissues was positively correlated with the DTPA-extractable form of the metals in the soil, but not correlated with the total.

You can use chelators as EDTA or DTPA

There are single chemical extraction (DTPA, EDTA) or you can try Diffusive Gradient in Thin-films (DGT) technique. It use a DGT tool to accumulate metals considered to be available for biota