Just bought the a new Bunn VPR with two heaters for work. Should the unit be unplugged at night? If it is unplugged, how long the next day will it take to brew a pot. Is it safe to leave the unit plugged in indefinitely?

You should call your vendor for service. Especially if it's on loan from them.
*** The following is for information only. Equipment should be serviced by a qualified tech. ***
VPS are pour over brewers. Like the 12 cup brewers you find at home, they need to be filled with 12 cups of water (a full pot), heated and then peculated over the coffee grounds and collected in a decanter.
BUT there is one main difference! The VPR and similar COMMERCIAL coffee machines are quick brewers. They usually have a pre-heated pot of water stored inside the machine.
* VPR's and similar machines REQUIRE a pre-fill and heating period prior to brewing. This means it's sitting on a level table and filled with water until water sprays from the brew head. At this point the unit is plugged in and the heater powers up. Brewer will pre-heat the water (there may be some water discharge from brew head as the water expands). Ready light will come on in about 15 mins.
* To Brew; Place coffee grounds in filter, place in funnel and brew head, clean empty decanter under funnel, slowly pour one full decanter of water (cold or hot) into brew tray. Do not overflow tray. Allow water level to sink before adding more water. Only fill with one pot as an equal amount will come out the brew head and funnel.
* FYI Coffee grounds are usually in pre-messured packets for office use. A simple guide is one tablespoon per cup. (level or heaping spoon is up to you)
* Since your brewer was bubbling at one point. I'm guessing it had water in the pre-heater at one time. But if it's not in use and left plugged in all that time then the water has probably boiled off. Hopefully someone unplugged the brewer prior to the unit blowing the thermal fuse.
* You can test the VPR by following the Pre-fill instructions I've listed earlier. If the brewer heats up and does not continuously boil (shorted condition) then try a brew. If it works then your okay. Otherwise the unit will need service for a blown high limit or bad heater element.
* Call your coffee vendor anyway. Many coffee vendors will service your brewer of even replace it as long as you buy coffee from them. Ask around.
* check bunn.com for free download of VPR manual

Aloha, ukeboy57

that is heating element problem...it is repairable but not for DIY..

Fill water tank until water comes out from sprayhead, THEN plug it in it should be OK.

IF the machine keeps blowing steam/keeps boiling the water, The thermostat is defective and must be replaced.

NOTE: If you don't use the machine for a couple days, UNPLUG IT. The water will evaporate if you don't unplug it.

Take off top of brewer after unplugging and check all electrical connections.If it is a older VPR it probably has a bad plug.You can cut off old plug and replace.You can pick up a new one at the hardware store.

VPS/VPR are pour over brewers. Like the 12 cup brewers you find at home, they need to be filled with 12 cups of water (a full pot), heated and then peculated over the coffee grounds and collected in a decanter.
BUT there is one main difference! The VPR and similar COMMERCIAL coffee machines are quick brewers. They usually have a pre-heated pot of water stored inside the machine.
* VPR's and similar machines REQUIRE a pre-fill and heating period prior to brewing. This means it's sitting on a level table and filled with water until water sprays from the brew head. At this point the unit is plugged in and the heater is turned on (CWTF's have a toggle switch behind the machine). Brewer will pre-heat the water (there may be some water discharge from brew head as the water expands). Ready light will come on in about 15 mins.
* To Brew; Place coffee grounds in filter, place in funnel and brew head, clean empty decanter under funnel, slowly pour one full decanter of water (cold or hot) into brew tray. Do not overflow tray. Allow water level to sink before adding more water. Only fill with one pot as an equal amount will come out the brew head and funnel.
* FYI Coffee grounds are usually in pre-measured packets for office use. A simple guide is one tablespoon per cup. (level or heaping spoon is up to you)
* Final; Getting back to unplugging when not in use. Yes there is a heater in the machine that keeps the tank warm. You can save power by turning off the warmer plates when not in use. Some units have up to 6 plates. The warmer "Blanket" is designed to keep the tank warm enough to brew and not waste heat or electricity. Yes unplug the unit at night if there is no night crew drinking coffee (or tea) But follow the Pre-heat instructions mentioned above prior to plugging the brewer back in. If the tank has been emptied at night or dried up after an idle week. Then there is a chance you may over heat and blow the thermal fuse. Or at best have a half pot short brew as the water dried up.
* Note leaving the brewer plugged in without brewing daily is not a good idea. The water evaporates and eventually drys out the pot. Takes about 1-2 weeks but it does blow the fuse(s) and the unit will need service.
* Final; Follow the Bunn set up and care instructions (manuals from Bunn.com for down loading. (*FREE*)
Aloha, ukeboy57

Your unit needs service. Contact the company that sold or installed the unit.

Possible the hi-limit turned off the heater, the thermostat is not working or the elements are damaged, or the inline thermal fuse is damaged.

Test that you have it plugged into an operating outlet.... Check that all of the switches are "on" (the warmer and the heater switches). If this doesn't help, you'll need to unplug the unit and test the switch and element for proper operation. Both can be tested for continuity. If they all test good, then I'd suspect the thermostat.
Good luck and best regards, --W/D--

Sounds like a leaking water pipe from the water source, unless you have a over temp heater and this results in steam and dripping.

Most likely it is your tank heater, but look on the top of the tank heater, because sometimes the wire will burn off the top of the element