Can someone help me translate that sentence. I can use 不好意思 or 对不起 in that situation, right?
Normally, when you ask for permission, you can just ask it straight in a question form. In your case, you wanted to ask "Can I post your photo on Facebook?" would become "我可以在Facebook上发布你的照片吗？"
To be polite and show humbleness, adding a simple 請問 (may I ask) is enough -- "請問我可以在Facebook上发布你的照片吗？" (may I ask, if I can post your photo on Facebook?)
To show more humbleness, add 不好意思 or 对不起 is appropriate. You are apologizing for intruding that person's space and taking up that person's time; for even request that person to pay attention to your request.
"不好意思 請問 我可以在Facebook上发布你的照片吗？" (excuse me, may I ask, if I can post your photo on Facebook?)
不好意思 or 对不起 are for apologizing, not asking permission. Apologizing is one possible function of 'excuse me', but that's not the sense you're using here.
A couple handy phrases that act more like 'ask-permission-excuse-me' are 劳驾 and 借光， but they're more appropriate when you're asking someone to do something for you, not when you're asking for permission to do something. For this example sentence, you probably want something like the “...你不介意吗” pattern. ('do you mind if...')
不好意思,对不起,may not be appropriate, 不好意思 sorry e.g. 不好意思，麻烦您了。for more choices users suggest looking up examples in online dictionaries, e.g. submit "can I" to LINE dictionary,relevant examples: 我也能来吗？我能借把剪刀吗？ 我能不能借枝笔？, submit "post picture":在一些论坛上你能张贴图片 ...我孩子吃脚趾头的照片贴出来, "facebook":请用脸谱（FACEBOOK）跟我联系。 我在脸谱网上看见了他 "excuse me" 请问这附近哪里有毛厕？
Excuse me, is it OK with you if I post your photo on Facebook?
'excuse me' here: 打扰一下， 请问一下， 请问
不好意思 is OK while 对不起 is not. In Mandarin Chinese 不好意思 is a subtype of "Excuse me", equivalent to the Cantonese 唔該. 不好意思 is a weaker version of "sorry" which can mean a minor disturbance to somebody, although it also means "unfortunate and apologies" after something bad happens. But 对不起 means a stronger "I'm sorry". It means you've done something wrong or you are determined to do something bad. Since you are negotiating, you could just use 请问 (May I ask) or 打扰一下 (bear me a minute) to be polite.
As a matter of fact, Facebook is 臉書, instead of 臉譜網. ‘臉譜’ means 'face mask'.
To make you sound more polite, you should use 'may' instead of 'can'.
So the sentence would be "(不好意思，) 請問我可以把你的照片放上臉書嗎？"
Hope this can help you :)