ご質問どうもありがとうございます。
様々な表現があると思いますが、いくつか自然な表現を紹介します。
1. I'm sorry, I didn't mean to scare you.
驚かせる意思は、ありませんでした！ごめんなさい！
2. Sorry, I didn't want to scare you.
驚かせたくはなかったんです。ごめんね。
1番目は、すこし丁寧な表現なのではないかと思います。
お好みに合わせて使い分けてみてください！
ご参考にしていただければ幸いです。
It happens to some people quite often that others don't here you coming. It seems you sneak up on people, especially when they are busy and not paying attention. The most polite thing to say is I didn't mean to scare you. Sorry I startled you is very commonly used after someone reacts to you arriving by jumping.
I didn't mean to scare you, startle you, frighten you, surprise you, make you jump....any of these are fine after the "I'm sorry"
You can always add "I didn't mean to"so they know it wasn't intentional.
これは、自分が近づいていることに相手が気付いていないとよくありますね。特に相手が忙しくて他のことに集中していると、その人に忍び寄るような感じになってしまいます。
最も丁寧な言い方は "I didn't mean to scare you"（驚かすつもりはありませんでした）です。
"Sorry I startled you"（驚かせてごめん）は、相手が自分が来たことにビクッと驚いたときによく使われます。
"I didn't mean to scare you/startle you/frighten you/surprise you/make you jump...." これらは全て "I'm sorry" の後に使えます。
"I didn't mean to" を加えると、わざとではなかったと伝えられます。
The literal translation to this phrase is "sorry to surprise you," but there are multiple ways of saying this expression and being grammatically correct. You could say:
1. I'm sorry I scared you.
2. I'm sorry I startled you.
3. I'm sorry if I surprised you.
4. I didn't mean to scare/startle/surprise you.
There are so many ways of saying this expression, and these are all perfectly natural ways of saying this phrase.
このフレーズの直訳は "sorry to surprise you" です。ただ、この意味の文法的に正しい言い方は他にもたくさんあります。
例えば：
1. I'm sorry I scared you.（驚かせてごめん）
2. I'm sorry I startled you.（驚かせてごめん）
3. I'm sorry if I surprised you.（驚かせてしまったならごめん）
4. I didn't mean to scare/startle/surprise you.（驚かせるつもりはありませんでした）
このフレーズの言い方はたくさんあります。上記は全てとても自然な言い方です。
After a surprise you may want to say sorry if for some reason the person you were surprising became scared.
When talking about surprises sometimes it can scare some people, so apologizing or saying you are sorry may make someone feel more at ease.
If you had surprised someone, and surprising them was an accident and you wish to apologize for what you had done, you can simply state, "I'm sorry, I didn't mean to scare you" or "Sorry for surprising you". Both of these sentences directly apologise for the fact that you scared this person and offers a sincere sorry for the outcome of surprising them.
相手を意図せずに驚かせてしまって謝りたいときには、次のように言えます。
"I'm sorry, I didn't mean to scare you"（ごめんなさい、驚かせるつもりはありませんでした）
"Sorry for surprising you"（驚かせてごめん）
どちらの文も、驚かせてしまったことについて誠実に謝罪しています。
The two sentences you see provided above are excellent ways to express to your listener that you are sorry for surprising them. In the second sentence you will see the term on purpose. This means someone does something intentionally. This term is appropriate for informal settings, like talking with family or close friends.
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