In reply to:
I know it depends one what else is running on the same server.
But is there any way to measure this?
I think you answered your own question. 
Without knowing what else is consuming bandwidth on the server, at that particular time, any answer to your question would be little better than a guess.
You could run a few tests to find the available downstream bandwidth, for example downloading largish files from your server, but the results would only be valid for that particular instant. The results may differ greatly during various times of the day and from day to day.
Mark
--
Save $50 on DreamHost hosting using promo code SAVEMONEY ( Click for promo code details )