The Mentorship thing looks like it'll be great. I feel inclined to join it, even though I've been RPing for a long while, just so I have access to help for FFXIV lore that I'm not 100% familiar with yet.
As others have said here, walk-up is intimidating. I've been shot down so many times, it's depressing. At least in WoW they had the add on MyRolePlay which flagged people as RPers and showed whether or not they were open to walk-ups and in character (assuming they updated it, which many did, religiously).
So, there's a few ways to approach it, depending on you and/or the situation.
1. Write up a 'troll' post. Trolling, in this case, by the definition rather than the common usage. If you're in a tavern or you're in the middle of nowhere and you think there's an RPer nearby that you'd like to RP with but you don't want to ask them OOC and arrange it, try writing up a post to show that you're an RPer.
 Siobhain Surtsthalwyn comes to rest from her long journey against the nearest wall. She mutters something to herself loud enough to be overheard, the tone of her voice belying her exhaustion. "Every gil... He took every gil." As though on cue a rumbling that carried farther than even her words sounded from within her toned stomach. The thunderous noise died off too slowly, turning her already pale carmine skin a deep red in mortification. (Some characters are kind enough to take this as an opening to walk up and offer some kind of aid at the sounds of hunger or concern overhearing she might have been stolen from. Admittedly, though, Siobhain is kinda huge so anyone who could successfully steal from her, most probably don't want to get involved with.)
 While maybe not a great post since it's an example, this is 'trolling' for me. It would draw, likely, someone's (who was within range and not terribly distracted by something else) attention. Many 'good' or 'lawful' or maybe even 'flirtatious' characters might be inclined to approach, for the reasons above. This might actually be a bit too subtle for some people, but when I'm up in the air about trying to RP and I don't want to go into OOC-zone, I'll post something like this that can catch the attention of another person. If they ignore her? She goes on her way. No harm, no foul. Most importantly, it's not something I have to retcon in the event no one notices it, like... a sword sticking through her gut.
 2. In some cases, like taverns mostly, people try doing something similar but they don't give any reason for someone else to walk up. If a character plops down in a chair and buries their nose in a book, chances are, no one is going to interrupt them unless they recognize them.Â
 However, if the character looks up after a while and focuses on one RPer, looking them over none-too-discreetly and paying attention to his or her conversation, he might find a reason to approach them or the constant, creeper staring might catch their attention. Be careful of overhearing whispers, though, many people consider it meta-gaming.
3. And of course, your other option, as per other suggestions, is to send a PM to the person and make sure they're open to walk up and not AFK or something.Â
Either way, I like to encourage people to be bold, even if their character's aren't the super social type. Find a plausible reason to walk up to a stranger-- what caught your eye about them in the first place?-- then go ahead and dive right in and don't be embarrassed if they're AFK or OOC or sad if they don't include you. Good RPers love when they're approached and many are too shy to approach others. Like K'nahli's example, you can leave a good impression on someone, even if they can't RP right that second.
As others have said here, walk-up is intimidating. I've been shot down so many times, it's depressing. At least in WoW they had the add on MyRolePlay which flagged people as RPers and showed whether or not they were open to walk-ups and in character (assuming they updated it, which many did, religiously).
So, there's a few ways to approach it, depending on you and/or the situation.
1. Write up a 'troll' post. Trolling, in this case, by the definition rather than the common usage. If you're in a tavern or you're in the middle of nowhere and you think there's an RPer nearby that you'd like to RP with but you don't want to ask them OOC and arrange it, try writing up a post to show that you're an RPer.
 Siobhain Surtsthalwyn comes to rest from her long journey against the nearest wall. She mutters something to herself loud enough to be overheard, the tone of her voice belying her exhaustion. "Every gil... He took every gil." As though on cue a rumbling that carried farther than even her words sounded from within her toned stomach. The thunderous noise died off too slowly, turning her already pale carmine skin a deep red in mortification. (Some characters are kind enough to take this as an opening to walk up and offer some kind of aid at the sounds of hunger or concern overhearing she might have been stolen from. Admittedly, though, Siobhain is kinda huge so anyone who could successfully steal from her, most probably don't want to get involved with.)
 While maybe not a great post since it's an example, this is 'trolling' for me. It would draw, likely, someone's (who was within range and not terribly distracted by something else) attention. Many 'good' or 'lawful' or maybe even 'flirtatious' characters might be inclined to approach, for the reasons above. This might actually be a bit too subtle for some people, but when I'm up in the air about trying to RP and I don't want to go into OOC-zone, I'll post something like this that can catch the attention of another person. If they ignore her? She goes on her way. No harm, no foul. Most importantly, it's not something I have to retcon in the event no one notices it, like... a sword sticking through her gut.
 2. In some cases, like taverns mostly, people try doing something similar but they don't give any reason for someone else to walk up. If a character plops down in a chair and buries their nose in a book, chances are, no one is going to interrupt them unless they recognize them.Â
 However, if the character looks up after a while and focuses on one RPer, looking them over none-too-discreetly and paying attention to his or her conversation, he might find a reason to approach them or the constant, creeper staring might catch their attention. Be careful of overhearing whispers, though, many people consider it meta-gaming.
3. And of course, your other option, as per other suggestions, is to send a PM to the person and make sure they're open to walk up and not AFK or something.Â
Either way, I like to encourage people to be bold, even if their character's aren't the super social type. Find a plausible reason to walk up to a stranger-- what caught your eye about them in the first place?-- then go ahead and dive right in and don't be embarrassed if they're AFK or OOC or sad if they don't include you. Good RPers love when they're approached and many are too shy to approach others. Like K'nahli's example, you can leave a good impression on someone, even if they can't RP right that second.
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