I have a slightly different solution to this. Instead of changing the rendering of the DataPager, I have slightly adapted the markup, and in terms of rendering, it still looks "bootstrap-like", even though it doesn't have the UL/LI tags with pagination class.
A very important thing (as explained in https://stackoverflow.com/a/19398488/1948625) is changing the class asp.net outputs for disabled control, it defaults to "aspNetDisabled" but for bootstrap it's much better to simply use "disabled". Do this in Application_Start in the Global.asax. If you don't, the first page, previous page, next page and last page buttons don't appear disabled.
void Application_Start(object sender, EventArgs e)
{
WebControl.DisabledCssClass = "customDisabledClassName";
}
Source: WebControl.DisabledCssClass Property (MSDN)
<asp:DataPager ID="it" runat="server" class="btn-group btn-group-sm">
<Fields>
<asp:NextPreviousPagerField PreviousPageText="<" FirstPageText="|<" ShowPreviousPageButton="true"
ShowFirstPageButton="true" ShowNextPageButton="false" ShowLastPageButton="false"
ButtonCssClass="btn btn-default" RenderNonBreakingSpacesBetweenControls="false" RenderDisabledButtonsAsLabels="false" />
<asp:NumericPagerField ButtonType="Link" CurrentPageLabelCssClass="btn btn-primary disabled" RenderNonBreakingSpacesBetweenControls="false"
NumericButtonCssClass="btn btn-default" ButtonCount="10" NextPageText="..." NextPreviousButtonCssClass="btn btn-default" />
<asp:NextPreviousPagerField NextPageText=">" LastPageText=">|" ShowNextPageButton="true"
ShowLastPageButton="true" ShowPreviousPageButton="false" ShowFirstPageButton="false"
ButtonCssClass="btn btn-default" RenderNonBreakingSpacesBetweenControls="false" RenderDisabledButtonsAsLabels="false"/>
</Fields>
</asp:DataPager>
Asp.net server markup above renders as this pager:

And this is the rendered html:
<span id="ctl00_Body_CaseList918421504_ListControl_Pager_it" class="btn-group btn-group-sm">
<a class="disabled btn btn-default">|<</a>
<a class="disabled btn btn-default"><</a>
<span class="btn btn-primary disabled">1</span>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl01','')">2</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl02','')">3</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl03','')">4</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl04','')">5</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl05','')">6</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl06','')">7</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl07','')">8</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl08','')">9</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl09','')">10</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl01$ctl10','')">...</a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl02$ctl00','')">></a>
<a class="btn btn-default" href="javascript:__doPostBack('ctl00$Body$CaseList918421504_ListControl$Pager$it$ctl02$ctl01','')">>|</a>
</span>