For most cases where one might "bump" a post in a bulletin board, the answer on LiveJournal is to make a new post, possibly one pointing back to the old one to revive discussion, or bringing the same topic from the old post up in a new post (sometimes linking back to the old one too.) Occasionally the answer is to leave a reply, or contact the original poster privately.
Let's examine some of the ways that people who are used to a bulletin board environment attempt to do things, and how and why they don't work.
Unlike a traditional bulletin board, commenting on an entry does not make that entry float to the top of the topics list. It may, however, bring it back to the attention of the person who posted it, the person whose comment you are directly replying to, and anyone who has subscribed to comments on that entry.
By default, you have a subscription to replies to entries you post and comments in your own journal. Most people seem to leave that turned on (but not everybody does). Also, the journal owner's Recent Comments page will show the most recent comments to their journal.
By default, you get notifications when someone leaves a comment in direct reply to your own comment (but not when someone comments in another part of that same entry).
People can choose to subscribe to all comments to an entry or thread that you are interested in and/or have participated in. Unlike a bulletin board environment, this does not automatically happen when one has participated. The user has to deliberately choose this option. As this is a relatively recent addition to LiveJournal's features, and one may only have a limited number of subscriptions, users tend to only subscribe to entries or threads they are particularly interested in, and/or delete older subscriptions to save room.
Sometimes, people create a style that gives links to some of the recent comment activity in their journal. Any style that has this has been custom-created; it is not a feature that LiveJournal offers, and they are using outside tools and/or scripting.
If you are thinking of attempting to "bump" by leaving a comment, consider the effect you want to have.
Do you want the attention of the journal owner, and/or anyone who has subscribed to the whole post? If so, leave a reply to the post itself.
Do you want the attention of a specific commenter or commenters to the post? If so, reply directly to their comments. Do not assume that someone else will check back to view other comments to the post after they have left their own comment. Sometimes someone will. Often someone will not.
It can be hard to find the right link to comment (to the whole post or to a specific comment) in some people's styles. If you are having trouble, try adding ?style=mine (or if there's already a question mark in the link you're viewing, add &style=mine) or ?format=light.
If you have a private comment or question for the journal owner or the person who posted in the community, send them a private message or find another place to get in contact with them. Do not comment and delete. If someone else has subscribed to new comments to that post, that person will also likely be e-mailed a copy of the whole comment.
If you want everybody who was likely to have originally seen the post to see your reply to it, the journal owner can post a link back to the original entry, or, if it was in a community, someone can post a link back to the original entry in the community. If it is not your journal or you do not have access to post to the community, you would have to ask the journal owner if they could do it, or ask someone who has access to post to the community if they could. However, unless the reply is very very important, the journal owner and/or community members may decline. Doing this excessively may also be looked on as "spammy" in some social groups.
Editing a Post.
Editing the text of a post only changes the text of the post. It does not otherwise notify anyone of anything. People who visit your journal or the community directly may see the edit if they're looking for it; people whose friends pages have not filled up past your entry may see the edit if they refresh the page; people who come back in response to comments may see the edit if they look through the original entry; people who come back just to look at the post and comments again may see the edit. It does not bump the entry's position on a friends page or send a notification to anyone.
Editing a Comment.
When you edit a comment, anyone who would have received a notification about the comment in the first place will get a notification that you have edited it. If you know you will be making several changes to a comment, you may wish to save them for one edit, rather than making several smaller edits.
However, once a comment has a reply, it can no longer be edited. Only paid accounts may edit their comments.
Changing the Date in a Community.
Editing an entry in a community to change the date will change where in the community's calendar/archive page the entry appears, but will not affect the entry's position on the friends page of community readers or in the main view of the community.
Changing the Date in Your Journal.
Editing an entry in your own journal to change its date will not change where it appears on the friends page of your readers. It appears on the friends page at the time the entry was originally posted to your journal (the time on LiveJournal's servers, not your computer's clock). An entry you post will only remain on the friends pages of your readers for two weeks, at which point it will fall off.
Editing an entry in your own journal to change the date will change where it appears in your journal's calendar/archive, as well as in the main view of your journal. If you set an entry's date to the future, it will remain at the top of your journal, to everyone who visits your journal directly. However, if you hope to gain attention to your post in this way, please be aware that many people use their friends pages and never visit the main page of your journal directly.
Additionally, editing the date of an entry to appear in the future can cause problems when posting entries later:
Using the Date Out of Order feature
The Incorrect Time Value Error and You.
Changing Post Security Significantly After Posting.
Posting something with a strong level of security and then editing it to a less restrictive setting will not change the entry's placement on the friends pages of your readers either. If you post an entry and edit its security within a few minutes of posting, your readers are likely to see it on their friends page unless their friends page is very busy indeed. If you edit its security a few days later, your friends may not see it unless they go all the way back to that day for some reason, or else visit your journal directly.