感谢@Wiktor Stribizew对regex的帮助，我想出了一个解决方案，但我不认为它像我期望的那样有效。如果你想出了更好的解决方案，请随时添加新的答案。

val boldRegex = Regex("(?<!\\*)\\*\\*(?!\\*).*?(?<!\\*)\\*\\*(?!\\*)")

@Composable
fun CustomText(text: String, modifier: Modifier = Modifier) {

    var results: MatchResult? = boldRegex.find(text)

    val boldIndexes = mutableListOf<Pair<Int, Int>>()

    val keywords = mutableListOf<String>()

    var finalText = text

    while (results != null) {
        keywords.add(results.value)
        results = results.next()
    }

    keywords.forEach { keyword ->
        val indexOf = finalText.indexOf(keyword)
        val newKeyWord = keyword.removeSurrounding("**")
        finalText = finalText.replace(keyword, newKeyWord)
        boldIndexes.add(Pair(indexOf, indexOf + newKeyWord.length))
    }

    val annotatedString = buildAnnotatedString {
        append(finalText)

        // Add bold style to keywords that has to be bold
        boldIndexes.forEach {
            addStyle(
                style = SpanStyle(
                    fontWeight = FontWeight.Bold,
                    color = Color(0xff64B5F6),
                    fontSize = 15.sp

                ),
                start = it.first,
                end = it.second
            )

        }
    }

    Text(
        modifier = modifier
            .fillMaxWidth()
            .padding(start = 8.dp, end = 8.dp, top = 12.dp, bottom = 12.dp),
        fontSize = 16.sp,
        text = annotatedString
    )
}

我认为它可以解决不使用第二个循环，但找不到它。
结果

Column() {
    CustomText(text = "This is a **bold** text")

    CustomText(
        text = "This is a **bold** text and another **random** value **build** with *regex expression"
    )

    CustomText(
        text = "This is NOT a ****bold** text build with *regex expression"
    )

    CustomText(
        text = "This is NOT a **bold text build with *regex expression"
    )
}

我用更少的代码和for循环对你的答案做了一些修改，你可以检查一下

val boldRegex = Regex("(?<!\\*)\\*\\*(?!\\*).*?(?<!\\*)\\*\\*(?!\\*)")

@Composable
fun TextWithBoldStrings(
    modifier: Modifier = Modifier,
    text: String,
    regularFontSize: TextUnit = 16.sp,
    boldSpanStyle: SpanStyle = SpanStyle(
        fontWeight = FontWeight.Bold,
        color = Color(0xff64B5F6),
        fontSize = 15.sp
    )
) {

    val keywords = boldRegex.findAll(text).map { it.value }.toList()

    val annotatedString = buildAnnotatedString {
        var startIndex = 0
        keywords.forEach { keyword ->
            val indexOf = text.indexOf(keyword)
            append(text.substring(startIndex, indexOf))
            startIndex = indexOf + keyword.length
            val newKeyWord = keyword.removeSurrounding("**")
            withStyle(
                style = boldSpanStyle
            ) {
                append(newKeyWord)
            }
        }
        append(text.substring(startIndex, text.length))

    }

    Text(
        modifier = modifier,
        fontSize = regularFontSize,
        text = annotatedString
    )
}