Is it good idea after weekly backup, to send the backup up drive or backup media to be kept in bank safe ?

 Yes It is good Idea

To keep your data in safe bank

If it is a Small backup you can keep them in the premises in an authorised secure place.

Its always better to have a off site backup for us to restore immediately without any down time.

Depends on the amount of your data. You have two cases, first, if you have a small data, you can backup them regularly. Second choice, It is impossible to have a backup if you have a terabytes. The solution is to use some big data technology which can tolerate errors for your data using duplicating your data over cluster of servers. Cloud  services can give you such a solution.On the other hand if you care about your data privacy, you can encrypt your data before upload them to the cloud

It's always safe and better to have off site backups once a week.

Whereas daily backup can takes place in the premises.