Is there a way to record a transfer so it doesn't show up as an expense?
Where is it showing as an expense? Are you using Windows or Mac? A transfer is not income or expense. You either enter the other account in the Transfer column or in the Category with square brackets like [Savings Acct].
I'm staying on Quicken 2013 Premier for Windows.
In a QWin report, click on the gear at the top right then on the Advanced tab, where there is a setting for transfers.
If you need finer control over which accounts are included, you can use the above in combination with selecting individual accounts to include on the Categories tab.
In QMac, you can enter the transfer account in the Transfer column and an expense category in the Category column. To record a transfer that is not an expense, you will want to use the special category "Transfer" in the category column. I think it's the same in QWin.
In QWin there is no Transfer column in a register and you can't assign a Category to a transfer. You can, however, assign a tax line item or a Tag.
If you want to assign a Category to money transferred between accounts, you would have to record it as 2 separate transactions, one in each account.