There are many ways to do this, but here is one using simple native features.
On the relationship "Contracts have many Bills", create a lookup field [Contract Price] so we can carry that value down from the parent table to the child table
On the Bills table, create a new formula field [Price Variance] that calculates [Contract Price] - [Bill Price]
On the Bills table, create a new report and use the [Price Variance] as a filter (is greater than 0) and this should provide you with all Bills that are greater than the contract price. Setup report subscriptions with the new report for automating the reports via email.