I would incubate 1ug/mL of the antibody in 4 mL of 5% BSA overnight at 4C together with 2ug/mL of the peptide. The following day I would centrifuge this at 5590 x g for 15 minutes at 4C to precipitate immune complexes. I would then proceed to use the supernatants to probe the membrane.
I have also tried this with Marvel/milk, but it doesn't work as well, as the milk kind of precipitates when you spin it down.
I am not sure why you want to use a peptide to test the specificity of a polyclonal antibody. Polyclonal antibodies are likely to have multiple antibody clones directed against at least several epitopes on your protein of interest. Your peptide is likely to present one or two linear epitopes for competition. You may see a reduction in signal but it is likely to not be complete.
The immune complex competition described by Silvia will only work if your peptide has two identical epitopes. If not, no complex will form.
I would first compete with the purified protein of interest, if it is available. Use a similar , but different protein as a control. Also, in your Western blot does the polyclonal only detect a single band. You need to know how the protein of interest shows up on a Western to understand the banding pattern. Also remember that you are detecting a denatured protein in the Western Blot format, so make sure your competition conditions reflect that.
I do agree with James about to use a peptide to test the specificity of a polyclonal antibody... you can do this, and it is relevant, with monoclonals..