By default TextMate will prompt you when a new version is available.

The Software Update page available via TextMate → Preferences… (⌘,) allows you to change Watch For to Nightly Builds which will increase the frequency, despite its name though, the there is no new build every night.

If you switch to Nightly Builds and there is an issue with one of the builds, you can switch back to Normal Releases and select Check Now, which then allows you to downgrade.

You can also find older builds in ~/Library/Caches/com.macromates.TextMate.