Thus being on a Mastodon Instance you can still mantain some relation with your previous Twitter account.
There are services like https://ifttt.com or https://crossposter.masto.donte.com.br/ than can connect your Twitter account with your Mastodon account.
With this services you can:
1) publish your tweets on Mastodon
2) publish your toots on Twitter
I strongly suggest to use only the second option, but that's my personal opinion.
Another thing you can do to help Twutter users to come to Mastodon is to use your complete Mastodon account address (name@instance) as your Twitter name