Honestly the best in terms of professional approach is to use Azure Data Factory and installation of Integration Runtime on the on premises.
You of course can use BCP but it will be cumbersome in the long run. A lot of scripts, tables, maintenance. No logging, no metrics, no alerts... Don't do it honestly.
SSIS is another option butin my opinion it takes more effort than ADF solution.
Azure Data Factory will allow you to do this in professional way using user interface with no coding. It also can be parametrized so you just change name of table name parameter and suddenly you are exporting 20, 50 or 100 tables at ease.
Here is video example and intro into data factory if you want to see quick overview. In this overview there is also demo which imports CSV to Azure SQL, you can just change it a little bit to make Azure SQL -> CSV and CSV > SQL server or just directly Azure SQL > SQL server.
https://youtu.be/EpDkxTHAhOs
It really is straightforward.