Is it OK to present a URL using a link shortening service such as bit.ly? The reason I'm asking is that I think it's a lot easier to enter this URL (e.g., if you read it in a paper) as opposed to full URL. Or is this a bad idea?
You should never offer a link shortener as the only option in an academic paper, for two reasons:
It's adding another point of failure: if the shortening service is down, then the link cannot be followed. This is a particular worry over time, since the service may go out of business.
One of the big reasons why link shorteners are so popular is that they keep track of usage statistics. I'd be offended if I thought an author was using this to monitor when the link was followed, where the people following it were located, etc.
So if you offer a shortened URL, it should only be in addition to the real URL, not in place of it. However, I'd tend to avoid even that. It doesn't look professional to me, and I don't think there's much savings for the reader. (Online papers should have clickable URLs, or at least ones that can be copied and pasted, so this only arises for someone who has a printed copy but no online copy. That can happen, but it's hardly a major issue.)
Short answer: It depends!
Long answer: Shortlinks are very useful when space is essential, i.e. when advertising something on twitter. Futhermore, they can often be used for analytics which some of those services offer.
Otherwise, it is often better to provide a full link. It looks more professional and gives more information. Since it is a link, it does not need to be typed in, so it might even be better to show a description instead of the link. The full domain also allows users to decide if they want to follow since it gives additional authenticity when the domain is well known. A lot of shortened urls lead to spam sites, or sites that try to introduce trojans.
A better alternative is to use a DOI if one is available. The providers of a DOI are supposed to ensure that the DOI is always up to date and points to the correct resource and as such a DOI is a better insurance against link rot than the original URL itself. DOIs are available for most recent papers (at least the ones I know of) as well as data etc. hosted on for example figshare and Zenodo. Apart from such resources, DOIs are generally not available and in that case I also recommend using the original URL directly.
I'm not sure what you mean when you say it's easier to enter. If someone is reading the paper online, it's a click (in the PDF) either way. And as @AM points out, link rot can then get you in two ways instead of one. In fact you should in general be leery about linking to URLs in a paper unless you have some belief that the URL will persist for the life of the paper itself.
I have no problem with shortening a link. In a paper, you won't risk your reputation just to have a spam or contained virus link, therefore people won't need to worry about the security. Also, I don't know if other services have this feature, but you can make an customized link as long as it is unique.
For example, this was my link to my dissertation: bit.ly/epHIVprotease. (Need not to follow it, I have pulled it down)
Anyone in my field will immediately understand what it says: electrostatic potential of a HIV protease. So it's also looked professional, I think.