How do I prepend a text to a file (the opposite of >>)?

You cannot do it with bash redirections alone; the opposite of >> does not exist....

To insert content at the beginning of a file, you can use an editor, for example ex: 

ex file << EOF
0a
header line 1
header line 2
.
w
EOF

or ed: 

printf '%s\n' 0a "line 1" "line 2" . w | ed -s file

ex will also add a newline character to the end of the file if it's missing.

Or you can rewrite the file, using things like: 

{ echo line; cat file ;} >tmpfile && mv tmpfile file
echo line | cat - file > tmpfile && mv tmpfile file

Some people insist on using the sed hammer to pound in all the screws: 

sed "1iTEXTTOPREPEND" filename > tmp &&
mv tmp filename

With bash version >= 4 , this can also be done using here-docs either on command line or inside a script.

PS: Has not been tested in other shells. 

newline="This is line -1"
cat <<EOF >a.txt 
$newline       #variables are accepted
This is line 0 #fixed string
$(cat a.txt)   #the old file - same name is ok
EOF

There are lots of other solutions as well.