Measuring transgenic gene expression with a microplate reader
Spectophotometry

Does the photometer allow using different wavelengths of light? Perhaps using a spectrophotometer might give you a control and your desired value, i.e. blue light may be absorbed by your sample, but red might not? The absorbance spectrum of the molybdenum-blue complex is very specific and you could use this to your advantage using spectral photometry.

Photometry + correcting for absorbance due to cell growth

Another approach is to quantify over time how your bacteria affect absorbance as a function of time and then subtract this from your experimental values.  For example, in a wellplate, place the following adjacently: use a (i) well without cells, and only arsenite in solution, (ii) cells without arsenite, and (iii) cells with arsenite. This should allow you to quantify quite accurately how much the arsenite, the cells, and how much both affect absorbance.

Of course as you say there may be an interaction between the cells and the arsenite slowing or speeding up cell growth, so that would be a pickle to disentangle. You could try, perhaps in the wellplates (this would be best!), to find out what effect arsenite has on growth and correct your final data this way.

Periodically sampling the solution; removing bacteria from the measurement

Another idea would be to culture your cells in arsenite, and take samples to obtain time-points. For each sample, you filter using small syringe filters (these are cheap and are typically used for sterilizing solutions, i.e. getting rid of bacteria but keeping the solution, given their pore size of ~.1 microns) and then perform photometry for the molybdenum-blue complex. This is typical practice in microbiology.

PCR? An idea.

Last but not least, it's good to remember this is an indirect readout of transgenic gene expression. Similarly, you could use quantitative PCR to quantify the expression of any transgenes - here, you use housekeeping genes as controls for cell number, and the mRNA expression of your transgene as the readout. You would be reading out the expression of mRNA, but I personally don't think it would be more 'indirect' than measuring arsenate concentrations in solution, especially when there are confounding factors and awkwardness in getting a clean measurement. The PCR approach would be quite accurate and likely more reliable.

These are just some initial thoughts - perhaps you could add a comment or we could chat about this if you think it could spark up some concrete ideas!