Couple items may help.
Firstly, the jquery-core.js file is located in the /CMSScripts/jQuery/jquery-core.js if you're on version 8+. The item in question (where you can use custom jquery) is available on 8.1, and forced on 8.2. So if you update your site to 8.2, by default the jquery-core.js is set to not overwrite the jQuery or $ variables. You can add your own jQuery to the header of the site and not worry about any conflict, i would HIGHLY recommend you do this.
Secondly, you can use a pre-existing Kentico template and try to fight against existing CSS and markup, but honestly it's pretty simple to 'start from scratch' and import a Bootstrap template yourself (include the css and if any js files in the header). Just head to the Page Templates and create a new master template, paste the template HTML header and footer (with a Page Holder in the middle), and have at it.
Thirdly, shameless plug, i created a Bootstrap layout tool, it's in the marketplace, if you import it you can design pages using bootstrap rows and columns, which should make designing your site and managing it a bit easier.