I'm not sure why you care to increase the Googlebot presence on your website unless you constantly dish out information that you need/want to get indexed instantly because it is time sensitive.
But, in any case, if you want the Googlebot to visit your site more often, then you want to get some more inbound links to your site. That will do the trick. The higher the PageRank of the source pages for the links the better. The more PageRank your pages have, the more often the bot tends to visit. To increase that, get regular dofollow links from pages with lots of Google PageRank.
Another way to get the bot to visit more frequently is to constantly add new content to your website, like all day long every day. Googlebot can be trained. If it always finds new content on a prominent page on your site then it will keep coming back more frequently to capture that new content. If it visits your page a bunch of times and sees that the content is not changing, then it decreases the number of visits and increases time in between visits.
Another way you can get it to visit is to change the parameters in your sitemap to tell it a certain page updates more frequently. But that only works for a short while as it soon learns whether or not you actually update that page very much. If you don't add new content to that page often, it will simply decrease the number of visits.
I don't even pay attention to how often Googlebot visits my sites. I don't much care. The only time it mattered to me was when I was running a news related blog.
