EMB-145 flight crew reported an engine bleed valve leak during climb out and a subsequent return to the departure airport.

Narrative

On climb out from ZZZ at about 1;600 ft. or 2;000 ft. or so; received EICAS warning bleed leak with associated engine bleed one valve displaying leak inscription. I passed radios off to FO (First Officer); who continued to climb via the SID as I ran the QRH. QRH resolved. Fuel was tight and with thunderstorms in the vicinity of our route to ZZZ1; so I realized we likely wouldn't have the fuel flying at 250 or be able to avoid icing conditions. Began to do my own calculations and hold. After three ACARS messages and about 25 minutes after first notification; dispatcher finally got back to me and agreed we did not have the fuel available. Held to burn off fuel to be at max landing weight to air return to ZZZ.ACARS responses could have been quicker; at least an acknowledgement would have been nice. Complete operations fail to begin with; as there was already a good spare aircraft at the maintenance hangar in ZZZ; and we were already delayed for four hours waiting for the flight that had diverted because they didn't have fuel to hold to wait for the thunderstorms that passed through quickly. Delayed all subsequent flights until the next day.