It depends. You cannot deduct it if it's a typical bed you can find in a store for the general public. However, if it is a special "hospital" type of bed/mattress, then you can deduct it.
Please see the following link for a comprehensive list of deductible medical expenses. IRS Medical Expenses
For medical expenses to be deducted on the tax return, you must itemize deductions on Schedule A, and your unreimbursed medical expenses must exceed 10 percent of your adjusted gross income (AGI). Then, you can only deduct the amount by which your unreimbursed medical expenses exceed this 10 percent threshold (7.5% of AGI for age 65 and older until 2017). However, some states allow the full deduction, even if you don't have enough for your federal taxes.
Where to enter medical expenses in TurboTax: While inside the software and working on your return, type medical expenses, sch a in the Search at the top of the screen (you may see a magnifying glass there). There will be a popup that says Jump to medical expenses, sch a. Select that to get to the general area.