It's strange because I've used Leaflet and Bootstrap together many times without encountering this conflict before. However, you're correct, there appears to be a conflict:
bootstrap.css:
img {
vertical-align: middle;
margin-bottom: 0px;
margin-top: 60px; /* this is causing the issue */
}
The bootstrap.css file adds a 60 pixel top margin to every image on your page, including images in your tilelayer. You can override this with custom styles like so:
div.leaflet-tile-container > img {
margin: 0;
}
However, it might be best to either re-download Bootstrap or use it from a CDN as I'm not experiencing this problem in this Plunker example:
http://plnkr.co/edit/fHtNdt?p=preview
This Plunker also uses Leaflet 7.3 and Bootstrap 3.2.2, which makes the situation even more confusing.