There is no bridge. I highly doubt the Twitter API TOS would even allow it. What you can do is get a client that supports both Mastodon as well as Twitter. I recommend Twidere on Android.
After the recent LinkedIn scraping court rulings, it seems Twitter should be legally scrapable. Twitter is largely public content submitted by their users, which Twitter does not own. It’s plausible this is why Instagram removed public access.
however, no-one but google actually has the horsepower to do it. You'll be playing an arms race with their devOps team if you try at scale, because they'll say you're degrading service and that IS illegal.
so, while it's a nice legal victory, it's a moot one for things like twitter.
It doesn't seem likely that Instagram or Twitter is going to go away tomorrow. Posting to Twitter and Mastodon means that eventually there would be content and interactions building up over time.
There seem to be two problems with replacing Instagram or Twitter. The first one is money to run servers, fight spam, handle subpoenas, etc.
The other one is having an authoritative directory. How is anyone to know that "ClearAndPresent" on Twitter is the same as "ClearAndPresent@SomeRandomInstance.mastodon"? An obvious way would be to send a DM to a Twitter account but it seems likely that Twitter would shut that down pretty quickly. We've all heard the stories of Facebook (and LinkedIn and ...) pillaging Gmail for contacts.
I actually have my twitter and mastodon accounts linked with this, but I assume a bridge like the other commenter requested would allow to follow any twitter acount from your Mastodon account.
https://f-droid.org/de/packages/org.mariotaku.twidere/