Using SFDonovan's code, you won't get the C_ID that matches the highest bidder. Instead, simply order by the bid amount:
SELECT C_ID, C_BIDCURRENT, ...
FROM currentoffers
WHERE C_LISTINGID=5
ORDER BY C_BIDCURRENT DESC
LIMIT 1
That query, assuming you fill in the ID and the rest of the column list, will get you the data related to the highest bidder.
Also, it looks like your script is vulnerable to SQL injection attacks. User-supplied data should never be placed directly into a SQL query! Instead, sanitize it with a function such as [man]mysql_real_escape_string/man (or, as is applicable in your case, you could cast the data to an integer or use a function such as [man]int_val/man - this is preferred, that way you don't get invalid data types that will break your query).