Q: Why does it seem to take them forever to draw comb on a frame (even with added wax) but it only takes a day or so to build a ton of burr comb in open places?
 
-K
 
A: Let me say first the I appreciate your question.
 
Bees have several rules they follow — They like to build comb following natures rules that has gone on for thousands of years.  Attach comb on some solid structure and build down attaching comb to other solid support.  This means comb is not built straight in nature.   We as humans have discovered that we can encourage them to build comb on foundation in frames so we can remove and inspect frames of straight almost perfect worker cell comb.  If you notice, new comb (burr comb) is often drone comb.  Since new foundation put into frames is worker cells, the bees will draw it in the case of a new hive started with foundation if spaces between frames does not exceed “The bee space rule” which allows bees to travel back to back on the surface of comb.  In our terms, that is a space 1/4 to 3/8 of an inch.  They do not usually fasten frames to the side walls of a hive for example that respects this bee space.
 
Bees usually build drone comb when there is a shortage of cells to produce drones.  Keep in mind that it takes less wax to produce drone comb cells than worker comb cells.  Drone comb cells are four cells to the inch while worker comb cells are five to the inch.  In nature comb is first constructed for the building of worker cells to receive eggs producing worker bees.  When a sufficient population of worker bees exist, honey bees will then add drone cells to the outer edge of comb they build.   We as beekeepers try to add 10 frames to start a new 10 box.  This removes most of the space to build as they naturally would.  It requires the bees to draw the foundation supplied by the beekeeper.  Sometimes a beekeeper will use only 9 frames in a 10 frame hive.  This allows more space between frames and thus, the bees begin to fill this space from the top down with burr comb.  This his a real problem if the foundation happens to be plastic or beeswax because the bees will build a comb between frames spaced too far apart. 
 
You may be surprised but when a good honey flow is on — lots of nectar available, the bees can draw wax at an alarming rate.  If you feed new bees with plenty of sugar syrup, they can draw 10 frames of wax (requires a good population of bees) very quickly.   With your question, I would guess they build the burr comb quickly because they lack the number of drone cells required by the hive.   How much is that?  A good strong healthy hive of bees will have a population of nearly 1000 or more drone cells.  Many beekeepers buy the green plastic drone comb to control Varroa Mites.  A frame of drone comb has about 2100 drone cells per side.  I have seen full frames — drone brood on both sides of the frame — drawn which if a queen started to lay in those cells would add about 4000 drones to a hives population if the frame is not pulled out and frozen to kill the brood and the varroa reproducing in drone cells.
 
Bees are truly amazing insects.  I hope this answers your question.
 
Dana Stahlman