New custom theme option (text input) giving index error

Wrap the call in an isset() conditional in this line:

<input id="cpt_theme_options[cpt_sm_dribbble_handle]" class="regular-text" type="text" name="cpt_theme_options[cpt_sm_dribbble_handle]" value="<?php esc_attr_e($options['cpt_sm_dribbble_handle']); ?>" />

Try something like this:

$cpt_sm_dribbble_handle = ( isset( $options['cpt_sm_dribbble_handle']) ? $options['cpt_sm_dribbble_handle']) : '' );

<input id="cpt_theme_options[cpt_sm_dribbble_handle]" class="regular-text" type="text" name="cpt_theme_options[cpt_sm_dribbble_handle]" value="<?php esc_attr_e($cpt_sm_dribbble_handle); ?>" />

EDIT

Note: your other alternative is to set default options on init, so that this option is set to some default value, e.g. an empty string.