Barcelona is about 580 kilometers from Torrevieja (to give you some idea, that is just a little less than London to Glasgow!), so even if you could find a tour it would also include a few nights stay in the city.

Driving would take anything up to 8 hours, with most of the journey on toll roads, a train would take about 5 or 6 hours from Alicante (Last time I went, in November the cost was around 80 Euro, but this fare will probably increase in the summer).

Your best option may be to fly. Vueling sometimes does some reasonable deals from Alicante. Or try http://www.rumbo.es

There are closer cities to visit!