STDOUT can be suppressed with "MyCommand >NUL"
STDERR can be suppressed with "MyCommand 2>NUL"

Most STDIO compliant DOS programs use STDERR to display error messages, so you'd have to suppress them (or log them) using the "2>" redirect. Unfortunately, in this case, Matt is getting a popup dialog box with an error. Unless there is something like this:
IF ERRORLEVEL 1 (NET SEND localhost "Error message")

Then it's probably an error that is being generated by Access as a result of an import macro that is missing its import file.

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GETTING A HANDLE ON REDIRECTION
If you’ve been exposed to C programming, you know that most applications write their normal output to a file handle called STDOUT. They usually write their error messages to STDERR. The values of these two file handles are 1 and 2, respectively. So the 2> symbol tells the command interpreter to redirect output meant for handle 2 (STDERR, the destination of error message output) to a specified file. Likewise, the 1> symbol can be used in place of the simpler > symbol to redirect output meant for handle 1 (STDOUT, the destination of normal output text) to a file. For example,
MYEXE > OUTPUT.TXT 2> ERRORS.TXT
is identical to
MYEXE 1> OUTPUT.TXT 2> ERRORS.TXT
Another file handle, STDIN, is typically used for keyboard input. Its file handle happens to be 0. Using the 0> symbol, you can get the same effect as piping output to another application. For example,
TYPE DIRECTRY.TXT | SORT
is equivalent to
TYPE DIRECTRY.TXT 0> SORT
Both use the output of the TYPE command to replace the input that SORT is expecting from the keyboard.

The 2> symbol is actually useful for gathering error output, but for clarity in your batch files, use the > and | symbols instead of 1> and 0>.