There is an unofficial BSC/xDAI to Polygon bridge, by xPollinate. A small fee is charged for using this service, which will be detailed for you before accepting the transfer.
Supported tokens for bridging:
During busy times, the Polygon MATIC exit liquidity on xPollinate may be insufficient for your desired amount. Keep refreshing xPollinate's homepage every so often, to check when there is enough liquidity for your transaction!
Other unofficial Bridges to Polygon bridges include ApeSwap, EvoDefi and Anyswap A small fee is charged for using this service, which will be detailed for you before accepting the transfer.
No bridge is required for this. You will need to register an account to use the exchanges. There may be fees associated with withdrawals. Exchanges only support deposits/withdrawals from specific tokens.
Always DYOR on the exchange, their supported tokens and fees!
If you'd rather not use any of those, you can try out this Coinbase route: