Bootstrap follows common web standards and—with minimal extra effort—can be used to create sites that are accessible to those using AT.
If your navigation contains many links and comes before the main content in the DOM, add a Skip to main content link before the navigation (for a simple explanation, see this A11Y Project article on skip navigation links). Using the .sr-only class will visually hide the skip link, and the .sr-only-focusable class will ensure that the link becomes visible once focused (for sighted keyboard users).
Due to long-standing shortcomings/bugs in Chrome (see issue 262171 in the Chromium bug tracker) and Internet Explorer (see this article on in-page links and focus order), you will need to make sure that the target of your skip link is at least programmatically focusable by adding tabindex="-1".
In addition, you may want to explicitly suppress a visible focus indication on the target (particularly as Chrome currently also sets focus on elements with tabindex="-1" when they are clicked with the mouse) with #content:focus { outline: none; }.
Note that this bug will also affect any other in-page links your site may be using, rendering them useless for keyboard users. You may consider adding a similar stop-gap fix to all other named anchors / fragment identifiers that act as link targets.
When nesting headings (<h1> - <h6>), your primary document header should be an <h1>. Subsequent headings should make logical use of <h2> - <h6> such that screen readers can construct a table of contents for your pages.
Learn more at HTML CodeSniffer and Penn State's AccessAbility.
Currently, some of the default color combinations available in Bootstrap (such as the various styled button classes, some of the code highlighting colors used for basic code blocks, the .bg-primary contextual background helper class, and the default link color when used on a white background) have a low contrast ratio (below the recommended ratio of 4.5:1). This can cause problems to users with low vision or who are color blind. These default colors may need to be modified to increase their contrast and legibility.