If you’re talking about clip-on bars on a standard road bike and, as you say, your position using them has been optimised and you’re not shipping excessive power, the usually quoted figure for time saved over a 40km TT is around two minutes.
However, if you do a bit of digging into this number, you’ll find that this is comparing a tucked position with aerobars to an ‘upright’ position with no aerobars. It’s very unlikely that you’d be riding in an upright position and it’s actually possible to get very aero on the drops or, even more so, in the ‘sphinx position’ on the hoods with your forearms horizontal.
So, we need to find the time savings on offer from riding aero on the hoods compared to riding upright on them. Again, over 40km, this equates to about 45secs. This means that the true saving of aerobars compared to a similar aero position on a bike without them is about 1:15mins. Not as impressive as the 2min saving but, considering the relatively low cost of a pair of aerobars, it still represents one of the best bang-for-your-buck aero savings.
Finally, key to harvesting these potential gains is to practise riding on your aerobars as much as possible and on real roads, not just the turbo.