How to send myself mail via bash script? sendmail: executable not found (adjust *mta* variable); Currently no active mailbox

in my bash script i have used mail command to send mail to remote server:

$ ./script.sh
mail: Cannot start /usr/sbin/sendmail: executable not found (adjust *mta* variable)
/home/me/dead.letter 8/378
mail: ... message not sent

when i changed remote recipient e-mail address to my current username (it is enough for the purpose), then no sendmail error, but i was not notified about new mail :-S

$ mail
mail: /var/spool/mail/me: No such entry, file or directory
mail version v14.9.19.  Type `?' for help
(Currently no active mailbox)
No more mail.
mail: There are new messages in the error message ring (denoted by ERROR),
mail:   which can be managed with the `errors' command
ERROR# ? 

I had to get away using Ctrl+D shortcut :-/

How to proceed please to let it send mail to myself?