Many distributions check the type of terminal before setting the prompt. Ubuntu, for example, contains this little gem in the default .bashrc:
# set a fancy prompt (non-color, unless we know we "want" color)
case "$TERM" in
Since screen uses its own TERM variable ("screen"), bash thinks it's not capable of displaying a fancy color prompt so it defaults to a simpler one. Screen is, of course, fully capable of the same complex prompts as a normal terminal.
So, to override this behavior, just hard-set your preferred PS1 options at the end of your
~/.bashrc file. Or, if you're feeling adventurous, find the test that checks the value of the TERM variable and modify it to accept "screen" in addition to "xterm-color".