There is one possibility to use that antibody. You can treat the dilute antibody during 1/2 hour with Blue-sepharose, take a look to the link below. The resin will capture the BSA (is able to capture 18 mg/ml of slurry). My advise, equlibrate the matrix with PBS. In a 15 ml tube add your diluted antibody (5 ug/ml may be a good coating concentration but it depends) and add 100 ul of PBS-pre-equilibrated matrix per milligram of BSA in your sample. Incubate half an hour in an orbital shaker to allow the biding of the albumin at RT. Centrifuge the tube for 2 minute at 3000 rpm. The antibody will remain in solution in the supernatant. You should be able to recover over 12 ml, the necessary to coat a 96-well plate with 100 microliter per well.  You can regenerate the Blue-sepharose and use it several times. I hope this helps (40 minutes protocol before starting your ELISA).     

http://www.gelifesciences.com/webapp/wcs/stores/servlet/productById/en/GELifeSciences-de/17094801

Another alternative is to do an ELISA sandwich with the antigen but not with two antibodies. If the antigen is cheap, recombinant or abundant is a good option if is an antigen what you want to detect. You can prepare your own conjugate following the protocol that I'm attaching and the idea of antigen sandwich ELISA is in the drawing I did a couple of minutes. I hope this helps. 

Dear Alonso, I would not recommend trying to remove the BSA, as you'll loose your stabilizer and you have not much information about how much antibody actually is present in your solution. I'd assume that the seller is trying to make as much out of his material as he can do, so expect almost no AB in the vial and when you purify it, you'll loose much due to absorption to surfaces, as the protein concentration is low. Don't dare to add a nonionic detergent as Tween 20, as it happily will block your ELISA wells, while you are trying to coat your plate....

However, in your situation, I'd contact the manufacturer if he could supply the AB without BSA.

Looking at the money you'll spend for preparing just one plate, I'd rather recommend to have your own polyclonal (!) antibody custom made (if you can wait for 2..4 month). Then you have 10..100mg quantities and you are able to prepare as many ELISA plates as you like.

If your are in a hurry and money plays no role, coat your plate with an antibody that will capture the species your AB is from, then you don't have to care about the BSA. But you might need about 1ug/well of your specific AB. And a second AB against your protein for the sandwich or a competitive antigen which is labelled with a reporter like HRP. 

Removing the BSA just before coating would not damage any antibody. BSA is the stabilizer and to impede protein aggregation when the concentration is high for long-term storage, but under 5 mg/ml IgG antibodies are quite stable in PBS. By the other hand, blue sepharose is used at industrial and lab-scale to purify antibodies with minimal losses, less than 1%. But it is true, if can avoid it, use another solution, but like everything, it is just to see if it work. Hope you find the optimum solution.