The receiving Roth IRA custodian will almost certainly not charge you anything; they are eager to get their hands on the money. In fact, the easiest and most efficient way is to fill out the forms for opening a Roth IRA account with the new custodian (most of this can be done online, but it might be necessary to print out a paper form, sign it and send/fax it to the company), tell them that the Roth IRA will be funded by a trustee-to-trustee transfer from the current custodian, and tell them to go get the money from the online bank who is the current custodian of your Roth IRA account. Don't approach your online bank and tell them to send the money to your new Roth IRA custodian; it will cost money and take more time and the likelihood of a screw-up is way too high.
The current custodian might charge you a fee for closing the account, or for "breaking a CD" if that savings account is a CD and you are withdrawing the money before the maturity date of the CD. This will be spelled out in the Roth IRA custodial agreement that you accepted when you opened the account (but most likely did not read in full when you received it, and might even have discarded).
One final note: with just $11K, please do not open a brokerage account for your Roth IRA and invest in stocks, bonds etc. For now, invest all your Roth IRA in a single low-cost mutual fund (preferably an index fund such as the Vanguard S&P 500 Index fund or Fidelity Spartan 500 fund); you can branch out into more funds when you have more money in your Roth IRA. Investing in these funds does not need you to have a brokerage account; you can do it directly on the fund's website. Avoid (for now) the siren song of Exchange-Traded Funds (ETFs) because you need to have a brokerage account to buy and sell them. When you have more money in your Roth IRA account, say in ten years' time, you can start investing in individual stocks, ETFs and the like through a brokerage account, but don't do it now.