You may also be interested in an answer to "How to accept payments via Ripple on a website".
It depends on if it makes sense to you to price your product or service in Bitcoin or in some other currency. For example, if your costs and profit margins are based in EUR then it makes sense to set your price in EUR (even if you'll later turn that into bitcoin). No matter what units/currency you denominate your price in, with Ripple people can pay using whatever assets they hold which Ripple can find a payment path for.
Assuming you want to set your price in bitcoin and end up with bitcoin in your private bitcoin wallet you could do something like the following:
- Create a Ripple address
- Chose one (or more) of the Ripple gateways that support bitcoin. You're looking for one that you trust to (temporarily) hold your bitcoin for you, that has low (or zero) fees, that has good liquidity, etc. Add trust lines to in BTC to that gateway for an amount that you are comfortable with (or to multiple gateways in various amounts).
- Use Ripple URIs on your site to help customers initiate Ripple payments with their client. The customer will then be given the option to pay with any of their assets for which paths exist.
- Periodically use the bitcoin bridge or withdraw via your Ripple gateway to get your BTC Ripple balance as bitcoin into your bitcoin wallet.
Alternatively you could use a service such as DividendRippler to attach a Bitcoin address to a Ripple address. Using DividendRippler you can generate a Ripple payment URI that sends BTC to their Ripple address with a destination tag generated for you and DividendRipple then forwards recieved BTC onto the blockchain to the address you've provided.