If I might link to Ilwe'ran's post here that has helped me in the past, not so much about walk-ups but about just generally initiating roleplay.
 The key is to have a reason to talk to someone. Like in real life, if you don't have a reason to talk to someone standing across the room, you won't do it. Giving your character a purpose to be there will also help give the conversation a bit of direction.
Going to events is especially helpful in that regard, as the purpose to be there is the event. You approach people and talk about whatever is going on and it's all very natural and expected.
 And as Seriphyn mentioned earlier, following 'real life' prompts can be helpful too. For example, when I go in to the local shop often people are talking about the weather, or might comment on how busy it is. While the conversation might take a little effort after that to get going (because talking about the weather can only last so long) both of you know that 'you're in. First step, complete.' That is where having a purpose to be there can help, because there's a hook for further conversation if the player doesn't provide one.
 If you're nervous, I've found the best thing to do is tell the other person. If you're worried about telling them, maybe consider approaching someone on this forum for walk-up RP first, because shyness is something that's often talking about on here, and most people are very understanding about it.
 Remember that it isn't anything personal if the RP doesn't go very well. Finding someone you really connect with won't always happen instantly, especially in walk-up situations, where you might not know much about the other's character. Sometimes it does, and you find someone you fit in with perfectly and conversation will flow easily. Often, you'll start talking to someone and realise they and you don't really have anything in common and it might be a bit awkward. Other times, you'll feel like there's some potential there and wouldn't mind seeing them again in the future.
 Was it your fault? No, just that people often don't connect because you're too different or a variety of different reasons (in this case, your characters haven't connected, nothing related to you IRL), or that person was distracted, or was busy doing something else.
 It's really difficult sometimes, but just need to keep trying.
 The key is to have a reason to talk to someone. Like in real life, if you don't have a reason to talk to someone standing across the room, you won't do it. Giving your character a purpose to be there will also help give the conversation a bit of direction.
Going to events is especially helpful in that regard, as the purpose to be there is the event. You approach people and talk about whatever is going on and it's all very natural and expected.
 And as Seriphyn mentioned earlier, following 'real life' prompts can be helpful too. For example, when I go in to the local shop often people are talking about the weather, or might comment on how busy it is. While the conversation might take a little effort after that to get going (because talking about the weather can only last so long) both of you know that 'you're in. First step, complete.' That is where having a purpose to be there can help, because there's a hook for further conversation if the player doesn't provide one.
 If you're nervous, I've found the best thing to do is tell the other person. If you're worried about telling them, maybe consider approaching someone on this forum for walk-up RP first, because shyness is something that's often talking about on here, and most people are very understanding about it.
 Remember that it isn't anything personal if the RP doesn't go very well. Finding someone you really connect with won't always happen instantly, especially in walk-up situations, where you might not know much about the other's character. Sometimes it does, and you find someone you fit in with perfectly and conversation will flow easily. Often, you'll start talking to someone and realise they and you don't really have anything in common and it might be a bit awkward. Other times, you'll feel like there's some potential there and wouldn't mind seeing them again in the future.
 Was it your fault? No, just that people often don't connect because you're too different or a variety of different reasons (in this case, your characters haven't connected, nothing related to you IRL), or that person was distracted, or was busy doing something else.
 It's really difficult sometimes, but just need to keep trying.
