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Welling manager Andy Ford was again left cursing his side's defending after they suffered a third successive Blue Square South defeat on Saturday.
The Wings boss made two changes following the midweek loss at Thurrock - but it was the same old story as both goals stemmed from cheap free-kicks given away on the edge of the Welling box.
Gethin Jones had a free header after 17 minutes to put Bath ahead.
Welling responded after the break and, after Ryan Johnson headed wide, Jake Hobbs (pictured) scored his second goal of the season after forcing the home keeper into an embarrassing error.
The Wings looked set to claim a point before more slack defending five minutes from time saw Chris Holland head home.
* Bromley suffered their second successive home defeat after losing 2-1 to Hampton & Richmond on Saturday.
The home side had taken a 19th-minute lead through Donal O'Sullivan - but goals in either half from Lawrence Yaku (27) and Craig Dundas (78) claimed all three points for the visitors.