Create the shortest BitShift
Mathematica, 343 bytes, 2573 characters
B=BitXor;t[a_]:={Mod[2a,256],⌊a/2⌋,a~B~1,a~B~128,0};w[a_,b_]:=Position[t@a,b][[1,1]];f=FindShortestPath[Graph[0~Range~255,e=Join@@Table[a#&amp;/@({}⋃t@a),{a,m=c=0,255}],EdgeWeight(w@@#&amp;/@e)],All,All];o=&quot;&quot;;u[a_,b_]:=(Do[o=o&lt;&gt;ToString[m=1-m],{If[a==b,6,a~w~f[a,b][[2]]]}];m=1-m);While[c~u~y;c!=y,c=f[c,y][[2]]]~Do~{y,ToCharacterCode@i};o

This is my first code competition. This program should generate the shortest possible program for any string. It effectively calculates a lookup table given the current state of the accumulator and the goal byte to find the shortest sequence of the five operations to get from any one to another, carrying the accumulator over characters and taking advantage of the size difference between instructions. Uses Mathematica 8's Graph infrastructure for calculating shortest paths (alternatives being to roll one's own or just embed the 256 x 256 table of instructions).
Ungolfed version (the first i = &quot;...&quot; line is also present, but not counted in the golfed version since it is the input):
i = &quot;This is a string, meant to test the effectiveness of your program. Here are some special characters to make matters interesting: Æ Ø ß. How meta! :D&quot;;
B = BitXor;
t[a_] := {Mod[2 a, 256], Quotient[a, 2], B[a, 1], B[a, 128], 0}
w[a_, b_] := Position[t[a], b][[1, 1]]
g = Graph[Range[0, 255], 
  e = Join @@ Table[DirectedEdge[a, #] &amp; /@ Union@t@a, {a, 0, 255}], 
  EdgeWeight -&gt; (w @@ # &amp; /@ e)];
f = FindShortestPath[g, All, All]; c = m = 0; o = &quot;&quot;;
u[a_, b_] := (Do[
   o = o &lt;&gt; ToString[m = 1 - m], {If[a == b, 6, w[a, f[a, b][[2]]]]}];
   m = 1 - m);
Do[While[u[c, y]; c != y, c = f[c, y][[2]]], {y, ToCharacterCode[i]}];
o

Output:
10111101111011110101000010110010101101101010000010110010110010010101101111110101001011001011001001010111110100110100110110101001000000101011101001101101010000000101011011101110111110111011010100110010000101011001101110111010100100001000001001010110011011101110101000010001000011011010100110100110010101111111001101010010001000010001000010010101101110111101101010011001000010010101100110010001000100010101110111101010000001101010010110010110010110010101100100010000110110101000000000110010101101001101001101001101010001000001011001001010110100110110101001100100001010111111001010110100110100110100110101000011010100100000101100100101011011111010100110100110100110110101001101110101001010110010001001010111011111101110110101000100001000010101111001001010110100110010001010111101111011010100010001000010110010101111011111001001010110100110110101001010110111111010100100010000100010001000100101011111011101111001010110010000001010110111011101110111110110101001101001101001101010010001000010010101100110111011101010000001010111010011010011010100110111010100110100110100110110101000001000100001101101010000010001010110111111101101010011010011010011011010100110111110011010100000000110010101100101100101011010011011010100101100101011110010010101101111101010001011001001010110100110010001010111100100101011011111010100100010001000001000100101011001011001011001001010110010001001010110111011110110101001000001010110111011101111101110110101001101110101001101111100100101011101111110111011010100001000001001010111011111110110101001101001101001101010000000110010101100100001011001001010111101111101010000010110010010101101001100100010101101111111011010100110111011010100010000100001010111011111010011011010100101100101011011010100100000010101101001101001101001101010011011101111001001010111111111001101010010001000010001000010010101101111101101010011001101111011101101010000010000100101011011111010100100010000100010000100101011011111011010100101100110010000101011010100010000010110010010101101001101010010010101101111110101001011001011001001010110011011101110101000100001010111011111010011011010100101100101011110010010101101001101101010011001000010101111001001010110011011101110101000010001000011011010100001000101011111110010101100100010001011010100110111111010100010110011010011010010101111110011010100100001000100010001000100101101010001100100101011111111001101010011010011010100110111011101111010011011010100101100101011111111100110101001000100001000100001001010110111011110110101001011001100100001010111111010011011010100001100101011011010100100010001000010001010111110111101010