The B is for 1st gear, basically. Only the higher line Mercedes had those.
The way your trans works is all normal. Putting into 2 at a stop will put it into first. Unless kickdown is activated (or 2 at the stop), car will start in 2nd gear.
It will shift out of 1st into 2nd, but not out of 2nd (if still in 2)... it will hit the rev limiter (not fun! I did this accidently once!!).
Also, if you are in 2 (but driving slowly in 1st gear), and you activate kickdown, then the car will be in 1st gear until redline or until the shifter is moved.
2006 E350 w/ 155k miles (Daily Driver)
1993 300E 3.2L Sedan w/ close to about 300k miles
2003 E500 Brilliant Silver (Had 217k miles when totalled!)
1989 300E with 289,000 miles (had for <1 yr while in HI)
03 CLK 500 cabrio (Mom's)
2006 C230k (Dad's)
1999 S420 (Mom's/Dad's)
2000 C230k Sport sedans
2001 CLK320 Cabrio (Mom's)
1995 C280 My First Mercedes-Benz... (155k miles. EXCEPTIONAL AUTOMOBILE. Was Very hard to let go of!)