Where can I buy bulk DUPLO sized bricks?
Duplo is less often stocked than normal LEGO, but this (US) Bricklink store seems to have quite some in stock. You might find other Bricklink stores in different parts of the world that have stock as well. 

Another option is looking for the 10622 Duplo Large Creative Box, which was on Black Friday sale at Walmart recently. It can still be found on Amazon and eBay, but contains many "other" kinds of bricks apart from your basic 2x4 and 2x2 bricks. Also, at ~$0.30 per brick (MSRP) this might not be your cheapest option - the Bricklink store I linked earlier has 2x2 bricks for as little as $0.12. Also check out last year's 10557 Duplo Creative Tower - it has more pieces (200 vs 193) and sells for less on Amazon currently.

You can also find bulk lots of Duplo bricks on eBay, such as this one. Price with shipping is still ~$0.30 per brick.

EDIT: Two more options:

1) If you're in North America, go look up a second-hand baby/children's clothing store like Once Upon A Child. I went there today and found several sealed bags and boxes with Duplo blocks. Common price was ~$6 for a bag. It was difficult to see what was in each item, but this might get you something.

2) You can look at Mega Blocks - their large bricks don't interconnect with LEGO or Duplo, but depending on what you are trying to do that might not matter. You could always stack them sideways, or modify them, or even (yikes!) glue LEGO bricks on top to make a connection.