A página man bash tem uma lista das seqüências de escape que você pode colocar em um prompt para que o shell as expanda. Procure em "Solicitação" e você encontrará esta tabela:
\a an ASCII bell character (07)
\d the date in "Weekday Month Date" format (e.g., "Tue May 26")
\D{format}
the format is passed to strftime(3) and the result is inserted into the
prompt string; an empty format results in a locale-specific time repre‐
sentation. The braces are required
\e an ASCII escape character (033)
\h the hostname up to the first '.'
\H the hostname
\j the number of jobs currently managed by the shell
\l the basename of the shell's terminal device name
\n newline
\r carriage return
\s the name of the shell, the basename of $0 (the portion following the
final slash)
\t the current time in 24-hour HH:MM:SS format
\T the current time in 12-hour HH:MM:SS format
\@ the current time in 12-hour am/pm format
\A the current time in 24-hour HH:MM format
\u the username of the current user
\v the version of bash (e.g., 2.00)
\V the release of bash, version + patch level (e.g., 2.00.0)
\w the current working directory, with $HOME abbreviated with a tilde (uses
the value of the PROMPT_DIRTRIM variable)
\W the basename of the current working directory, with $HOME abbreviated
with a tilde
\! the history number of this command
\# the command number of this command
\$ if the effective UID is 0, a #, otherwise a $
\nnn the character corresponding to the octal number nnn
\ a backslash
\[ begin a sequence of non-printing characters, which could be used to
embed a terminal control sequence into the prompt
\] end a sequence of non-printing characters
O que você quer é \ w, então faça
PS1="\w $ "
Isso mudará para o shell atual. Você pode colocar a definição em seu .profile para que ela fique firme.