I don’t live in the US anymore. Can someone from US mail my tax return to IRS? If I do, they might not get there in time.

[Karinagoia]

I still have an active US bank account

[CarolynM]

Yes,someone in the US can mail your tax return, but you would have to give them access to your account to print the return to mail. 

Even if you live abroad, you are still eligible for e-file if you would like to try that first.