To make changes to, or remove the navigation bar you will need to access the 'Manage my store' section of your eBay account.

1. Navigate to, My eBay > 'Manage my store':

2. In the left-hand Store Management menu, click 'Display Settings':

3. In the Theme and Display section, you will need to click 'Change' on the section labeled 'Left navigation bar settings':

4a. This section will look like this:

This section is fully labeled and described for ease of use. When you un-tick a component you will see the result show instantly in the right-hand example image. 
In the image for 4b. you will see the 'Search box' component has been deselected. 

4b. When you have decided what changes you wish to make and have made the selections to the relevant tick boxes click 'Save Settings' at the bottom of this page: