Is there a way to bridge out bitcoin testnet to bitcoin signet?
If you create the same coinbase transaction in both networks, then yes, those coins will be connected. The same trick is possible even between regtest and mainnet, see:
https://bitcointalk.org/index.php?topic=5479988.msg63437260#msg63437260Also, there are other ways. In general, if people can trade between Bitcoin and altcoins, then you can use the same tools to do the swap between testnet and signet. For example: both parties can open 2-of-2 multisig channels on both coins, and then swap them, by closing those channels.
But I wonder: why do you need to swap anything, if you can produce coins on your own CPU? In case of signet, you can just change signetchallenge into OP_TRUE. And in case of testnet3, you can just locally connect two nodes, ignore the outside traffic, and simply put your system clock 20 minutes forward (and then, any block with the minimal difficulty will allow you to test mining).