I'd never read anything into the fact that someone has logged into the site. There's every chance that the person I've contacted might have had a chance to read my message, but might not be in a position to reply straight away. They could be at work, on the bus, on their phone around family and friends and so on, sneaking a quick peek. They might want to think a bit before responding, and perhaps see what else you've posted and read that, etc. There's also the timezone issue.
I think my instinct is never to chase anyone for responses - for RP enquiries or posts. I guess my view is that anyone I have to chase for a response probably isn't interested, or probably isn't interested enough to be a good prospect for a RP. Or too busy. I'd rather not prod someone into a token, polite response only for discussions to fizzle later. Having said that, I'm always open to people coming back to me later on, or resuming discussions after a gap. We're all busy.
The other thing I wonder about is whether things are different depending on how 'in demand' the RT author is, and how many responses they get. I probably get one response per three RT bumps, and they're almost always good quality in the sense of having read my RT and responding thoughtfully. We don't always end up matching, but that's another issue.
But I get the impression that other people get a lot more responses. Especially women playing female characters. From some of the stories I've heard from RP partners, I get the impression that some guys aren't good at taking rejection - even when it's phrased very carefully - and will continue to push and pester, and perhaps even get abusive. There's also presumably a reason why a lot of female RTs have some kind of code word/ Van Halen M&Ms thing to mention to prove you've read it - lots of low quality, poorly targeted, spammy responses.
In my decade plus RP experience (as a male playing male characters), I've only ever had one angry/abusive response to declining to RP with someone, and only one RP ending a bit huffily. That's it. I'd be amazed if that would have been the case if I were female playing female characters.
So... when I respond to RTs, I do so in the expectation that anyone I want to RP with is going to get a lot of high quality responses. That the RT poster won't know if I'm the kind of person who takes rejection well, without pestering, and may not feel comfortable engaging at all if the answer is no.
I probably get responses about half the time, of which half-to-two-thirds of those fizzle quickly. So I think my strategy is not to invest too much in initial responses to RTs. A link to mine, a paragraph or two about what I liked about their RT, how/why I think we might be compatible, any reasons why we might not be, something about deliberately keeping my opening message short because they're probably swamped.