Anytime police have to ask for your permission to do something, it's because they don't have the right to do it in the first place. Don't make their job any easier. If they ask you if it's ok to come into the house, or if it's ok to search your car or your purse, you may politely decline. Do not resist if they insist on doing what they want, and certainly if they show you a warrant, but if they ask you for your permission to search anything, calmly and politely make clear that you decline the request and do not consent. They may use words like "I'm just going to look in your bag here if it's ok", or "Mind if I step in and have a look around"? Whatever words they use, politely decline and make clear that you do not consent.
You have a Constitutional right to be free from unreasonable searches. The penalty for violating that right is that any evidence seized by police in this manner must be suppressed. Your lawyer accomplishes this by filing a Motion to Suppress (in Washington, it's called a "3.6 Motion", in California this is called a "1538.5b Motion"). When evidence is suppressed, the case is often dismissed completely because there is no longer any evidence available for prosecution. If you have consented to a search, you've given up your rights and your lawyer will not be able to file the Motion to Suppress. Don't throw away these opportunities, never consent to a search.