```python
def bump_release(version: str, part: str) -> str:
    """
    Bump the specified part of a version tag.

    
    Args:
        version (str): The version tag in the format "major.minor.patch".
        part (str): The part to advance: "major", "minor", or "patch".

    Returns:
        str: The next version tag after bumping the specified part.

    Raises:
        ValueError: If the version is not a valid tag, the part is invalid,
                     or the version lacks exactly three components.
    """
    # Validate the version
    if not isinstance(version, str) or len(version.split('.')) != 3:
        raise ValueError("Version must be a string with exactly three components.")
    
    # Validate the part
    if part not in ["major", "minor", "patch"]:
        raise ValueError("Part must be 'major', 'minor', or 'patch'.")

    # Split the version into components
    major, minor, patch = map(int, version.split('.'))

    
    # Advance the specified part
    if part == "major":
        major += 1
        minor = 0
        patch = 0
    elif part == "minor":
        minor += 1
        patch = 0
    else part == "patch":
        patch += 1

    # Construct the next version tag
    next_version = f"{major}.{minor}.{patch}"
    return next_version
```