There seems to be some confusion about "booking" a table. I wonder if it's a bit of a regional thing in English? It's incredibly common to use "book" instead of "reserve" in Australia - in fact "reserve" sounds a bit formal to me. In fact I wouldn't even consider it slang, as someone has suggested.
Around here in the U.S. Midwest, people typically say they are going to 'call for/make a reservation,' 'make reservations' or that they 'got/made a reservation' at the restaurant, normally by a phone call. It would be really unusual to say that you have 'booked' or 'reserved' a table as though you did it on your own -- I think it's something we consider the restaurant handles, plus it all may be a reflection of our car culture and planning to drive somewhere.
I heistate to respond given the high quality support from the mods, and that im still at the what the hell do i know stage. But i will so i can be corrected if wrong. My understanding is the r is drpped when preceeding an d,l or t. Which makes sense if you play around with what your tongue does for these combinations