Using a custom php.ini for your bot and adding the following directiv will archieve what you want:
error_log = log/php_errors.txt

In addition you need to make sure you have error logging enabled
log_errors = On

Aside from that, the level of errors you want to be reported
; This directive informs PHP of which errors, warnings and notices you would like
; it to take action for. The recommended way of setting values for this
; directive is through the use of the error level constants and bitwise
; operators. The error level constants are below here for convenience as well as
; some common settings and their meanings.
; By default, PHP is set to take action on all errors, notices and warnings EXCEPT
; those related to E_NOTICE and E_STRICT, which together cover best practices and
; recommended coding standards in PHP. For performance reasons, this is the
; recommend error reporting setting. Your production server shouldn't be wasting
; resources complaining about best practices and coding standards. That's what
; development servers and development settings are for.
; Note: The php.ini-development file has this setting as E_ALL | E_STRICT. This
; means it pretty much reports everything which is exactly what you want during
; development and early testing.
;
; Error Level Constants:
; E_ALL             - All errors and warnings (includes E_STRICT as of PHP 6.0.0)
; E_ERROR           - fatal run-time errors
; E_RECOVERABLE_ERROR  - almost fatal run-time errors
; E_WARNING         - run-time warnings (non-fatal errors)
; E_PARSE           - compile-time parse errors
; E_NOTICE          - run-time notices (these are warnings which often result
;                     from a bug in your code, but it's possible that it was
;                     intentional (e.g., using an uninitialized variable and
;                     relying on the fact it's automatically initialized to an
;                     empty string)
; E_STRICT          - run-time notices, enable to have PHP suggest changes
;                     to your code which will ensure the best interoperability
;                     and forward compatibility of your code
; E_CORE_ERROR      - fatal errors that occur during PHP's initial startup
; E_CORE_WARNING    - warnings (non-fatal errors) that occur during PHP's
;                     initial startup
; E_COMPILE_ERROR   - fatal compile-time errors
; E_COMPILE_WARNING - compile-time warnings (non-fatal errors)
; E_USER_ERROR      - user-generated error message
; E_USER_WARNING    - user-generated warning message
; E_USER_NOTICE     - user-generated notice message
; E_DEPRECATED      - warn about code that will not work in future versions
;                     of PHP
; E_USER_DEPRECATED - user-generated deprecation warnings
;
; Common Values:
;   E_ALL & ~E_NOTICE  (Show all errors, except for notices and coding standards warnings.)
;   E_ALL & ~E_NOTICE | E_STRICT  (Show all errors, except for notices)
;   E_COMPILE_ERROR|E_RECOVERABLE_ERROR|E_ERROR|E_CORE_ERROR  (Show only errors)
;   E_ALL | E_STRICT  (Show all errors, warnings and notices including coding standards.)
; Default Value: E_ALL & ~E_NOTICE
; Development Value: E_ALL | E_STRICT
; Production Value: E_ALL & ~E_DEPRECATED
; http://php.net/error-reporting
error_reporting = E_ALL

Please note that we are in the process of cleaning up the BeBot codebase and that especially for 0.6 there are quite a few calls to depreciated functions as well as numerous notices.