As stated in another answer, you should be able to export your wallet seed from electrum and use it in breadwallet. However, this may not be the best way to do things.
Think of storing and using bitcoin the same way you think of storing and using fiat currency. Normally you have a relationship with a bank (or several), where you have several accounts set up. Typically one is for your savings, and one is for checking (day to day use). The checking account will have a card you can use for purchases as well as a checkbook for paper payments. In addition, you also carry a wallet where you keep a small amount of cash for various uses.
The point is, there are several levels of the security/convenience tradeoff. Your savings account is more difficult to access than your checking account, which is more difficult to access than your cash. The bulk of your money should be in savings, with a smaller amount in checking, and the smallest amount as cash. This way if you lose your wallet, you haven't lost your life savings. Think of bitcoin wallets likewise.
There is nothing wrong with maintaining a "savings" wallet and "back pocket" wallet. One is kept more secure and holds more funds, while the other is carried with you and used regularly. You can even have more levels, such as a paper wallet with retirement savings.
Always be in a position where dropping your phone in a toilet won't cause financial ruin.