Generally the very cheapest way to acquire new bricks is to buy large “classic” boxes on sale. Famously the best set for this is the 10654 Classic XL Creative Brick Box. It’s a 1600 piece set of generic bricks in a handful of colours. It’s currently retailing for $88 in Australia giving a per-piece price of $0.055 – not that much more than my average for bulk purchases. This particular set is exclusive to Toys R Us. They have reasonably frequent “buy one get one half price” sales, so if you want two or have a mate to go in with, that brings the part price down to just over 4 cents.
If you can’t wait for that, looking for a Lego sale at one of the major retailers and doing the sums on the larger classic boxes is generally the way to. I was checking out at Myer on-line a week or so ago with a Classic box set with a per piece price just over four cents only to have it fail with an out of stock message even though it looked in-stock in the on-line catalogue. The next best option was this set coming out at 6 cents per peice.