I have been on the look for a very cheap and fast way to do some cross-bridging between Ethereum and Layer 2 networks without using risky third-party bridges?
Your only choice is using the native bridge. However, it may be costly because you must pay all the fees to do your transaction. The only best way to use third-party bridges. It's too costly for me to paid 20 bucks just for a transaction.
I have often bridged my funds. I have tried native bridges from Optimism, Arbitrum, and even Blast.
The only way for you to remove the third-party bridge is to use the L2 developer's own bridge. I don't even see another possible solution for this.