AFAIK, there is no direct API but you can access social:rootCommentSystem property of the blog id using your logged in user.
e.g for blog id '/content/usergenerated/asi/jcr/content/we-retail/us/en/community/blog/jcr:content/content/ primary/blog/layer-it-on'
social:rootCommentSystem is
/content/we-retail/us/en/community/blog/jcr:content/content/primary/blog
The blog site url will be this path till jcr:content and add .html to render it. i.e. /content/we-retail/us/en/community/blog.html will render the blog site for you.
Alternatively, you can also access top level resource of a blog id by commentObj.getTopLevelResource() , which will essentially give you same as social:rootCommentSystem and than you can proceed as above.
The blog site URL path is also present in basePageURL. This property will be available to you while rendering blog id and you can see this in the entry_topic.hbs. If you have to use it while rendering the blog id only, this will be your best bet. Overlay hbs file and use basePageUrl, wherever you want to use,
I want to add that if you have to use this, overlay or extend(preferrably) blog instead of doing in OOTB components.