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If the number of serach termes becomes large, it would be better to use a StringBuilder. Otherwise, a new string (which is growing) will be allocated for each iteration.

I would consider to cache results:

public string BinarySearchSetup(long[] data, long[] searchTerms)
{
    var lowerBound = 0;
    var upperBound = data.Length - 1;

    var cache = new Dictionary<long, long>();
    var resultBuilder = new StringBuilder();
    for (var i = 0; i < searchTerms.Length; i++)
    {
        var searchTerm = searchTerms[i];
        long result;
        if (!cache.TryGetValue(searchTerm, out result))
        {
            result = BinarySearch(data, lowerBound, upperBound, searchTerm);
            cache.Add(searchTerm, result);
        }
        resultBuilder.Append(result);
        resultBuilder.Append(" ");
    }
    return resultBuilder.ToString();
}

If you have a really large list and multiple cores, you could also try to parallelize the search, e.g. using Parallel.For in combination with an CuncurrentDictionary for caching:

public string BinarySearchSetup(long[] data, long[] searchTerms)
{
    var lowerBound = 0;
    var upperBound = data.Length - 1;

    var cache = new ConcurrentDictionary<long, long>();
    var resultArray = new long[searchTerms.Length];
    Parallel.For(0, searchTerms.Length, i =>
    {
        var searchTerm = searchTerms[i];
        long result;
        if (!cache.TryGetValue(searchTerm, out result))
        {
            result = BinarySearch(data, lowerBound, upperBound, searchTerm);
            cache.TryAdd(searchTerm, result);
        }
        resultArray[i] = result;
    });
    return string.Join(" ", resultArray);
}