dotConnect for BigCommerce does not support transactions because BigCommerce itself doesn't support them. All data modifications are immediately sent to BigCommerce. They cannot be performed offline, unlike selecting of cached data. Only after they are performed on the BigCommerce account, the cache is updated (if the cache for the table being updated exists). If necessary, calculated or system field values are queried from the server after data modification is performed, and cache is updated with these values.
All these actions are performed implicitly by dotConnect for BigCommerce itself. You don't need to do anything special, just modify data in the same way as with any other ADO.NET provider. However, remember that there are some limitations on DML statements in dotConnect for BigCommerce. These limitations along with the details of the DML statement execution by dotConnect for BigCommerce are described in the Execution of DML Statements topic.