Move to the printable ASCII front

Ostrich, 46 45 chars

Don't have a version number in the header because this is actually just the latest commit. I added the O (ascii code to string) operator after releasing the latest version (but still before this challenge was posted).

{a95,{32+O}%:d3@{:x\.3@?3@\+\x-x\+}/;{d=}%s*}

Explanation:

a             this is the "r" array (a is short for [], empty array)
95,{32+O}%:d  this is the "d" array
3@{...}/      for each character in the input (as an "argument")...
  :x            store in variable x (stack is now [r d c])
  \.3@?         find index in d     (stack is now [r d idx])
  3@\+          append index to r   (stack is now [d modified_r])
  \x-           remove char from d, and then...
  x\+           prepend char to d   (stack is now [modified_r modified_d])
;             throw away modified_d
{d=}%         map r to indices of (original) d
s*            join (s is short for ``, empty string)

CJam, 20

'¡,q{_C#c' ,C+@|}fC;

Try it online

Explanation:

'¡,      make a string of characters with codes from 0 to 160 (a modified "d")
         could have been to 126 but stackexchange doesn't like the DEL character
q        read the input (s)
{…}fC    for each character C in s
  _      duplicate the d string
  C#     find the index of C in d
  c      convert to character (this is the result)
  ' ,    make a string of characters from 0 to 31
  C+     append C to the string
  @      bring d to the top
  |      set union, preserving order; effectively, C is moved to position 32
         this is the updated d string
;        pop the last d

SWI-Prolog, 239 197 189 bytes

a(S):-l([126],X),a(S,X,[],R),b(R,X).
a([A|T],X,S,R):-nth0(I,X,A,Z),(a(T,[A|Z],[I|S],R);R=[I|S]).
b([A|T],X):-(b(T,X);!),nth0(A,X,E),put(E).
l([B|R],Z):-A is B-1,X=[A,B|R],(A=32,Z=X;l(X,Z)).

Example: a(`Two more questions and I have bzip2 in less than 100 bytes!`). outputs:

Twp#o"si$sv#uvq(u$(l#o#W!r%w+$pz,xF%#,"x(. #0--'$GG ".z(**:

(and true . after it, obviously)

Note: your SWI-Prolog version has to be one of the newer ones in which the backquote ` represents codes strings. Code strings used to be represented with double-quotes " in older versions.