How can I shorten the bash prompt's current path to one letter per directory?

After playing with this for a while I got the answer you require:

Add this to your .bashrc file in your home directory, exit the terminal and renter it and you will get you prompt.

PS1='$(eval "sps")$ '
sps() {
   echo "$PWD" | sed -r 's|/([^/]{,2})[^/]*|/\1|g'
}

It uses the declared function sps() to evaluate the path every time the variable PS1 which is the prompt, is displayed

ie

/ho/de/De/Ap/Ti$ pwd
/home/deth/Desktop/Apps/Tivo
/ho/de/De/Ap/Ti$ 

Or...if you insist on the one letter

PS1='$(eval "sps")$ '
sps() {
   echo "$PWD" | sed -r 's|/(.)[^/]*|/\1|g'
}

Which displays:

/h/d/D/A/T$ pwd
/home/deth/Desktop/Apps/Tivo
/h/d/D/A/T$ 

To truncate all directory names except the last one:

PS1='$(eval "sps")$ '                                                                                
sps() {                                                                                              
    python -c "import sys; dirs = sys.argv[1].split('/'); print '/'.join(d[:1] for d in dirs[:-1]) + '/' + dirs[-1]" $PWD
}

shorten all names except the last one without python:

user:/h/u/D/C/current$ 

sps() {
    echo `dirname $PWD` | sed -r 's|/(.)[^/]*|/\1|g'
}
PS1='\u:$$(eval "sps")/\W\$ '