It's not logical to have a bundle item with fixed price and keeping child product with their default price. Magento is not written on that logic because when you want to apply discount, it will get messed up.
However, you can get it done with little tweak, which needs you to enter prices of each child product manually.
Choose Price as Fixed while creating bundle product and then you can add child product's price manually.
So if you set a bundle's price (initial) as $100 and each child product's price $10, $20 $30 etc, then when user chooses each option on front end system will keep adding these child product's prices.
Remember, this approach is not the best practice, because when a child product's prices changes then you have to come to bundle product and change manually one by one.
Hope this helps.