OK got it. I would not want to walk from the airport to your B&B, especially with luggage. Fortunately there is a bus at the airport that will get you close.
I would recommend getting off at Mestre and taking the No 15 bus to the airport. It runs every half hour on the hour and at 30 past, it takes about 24 minutes. At the airport, change to the No 45 bus that will take you to the end of the street where your B&B is. I don't know if this is free transfer.
To get into Venice take that No 45 bus back to the airport, or maybe walk it now you don't have luggage and know where you are. at the airport take the No 5 bus to Piazzale Roma.
I'm digging up the schedules now and will post back.
Edit: If it is a Sunday, the No 15 bus runs hourly at 6 past the hour.
Edit 2: Here is the web page with links to all the Venice suburban bus lines listed by bus number. each has a clickable pdf of the schedule and a route map. The lines you want are the No 5, No 15, No 45. I have confidence you can figure them out if you can bus timetables.
http://actv.avmspa.it/node/741
It looks like you get a free transfer as long as you complete your journey in 75 minutes. The bus from Mestre FS (that is how it is shown on the schedule) to your B&B (Triestina-Civico Poste "208" on the map, just Triestino on the schedule) is 1.50 Euro.
Getting into Venice from the airport, it is 8 EURO each way. You're paying tourist prices now. If you just want to walk your good. If you want to ride a vaporetto, which I highly recommend, it is 7.50 EUR each ride. So if you went in from the airport rode the vaporetto to somewhere like Piazza San Marco, then returned the same way, it will cost 31 EUR. There is a 24 hour vaporetto pass that includes a round trip bus ticket to/from the airport available for 32 EUR. It will save time because you have to scan the pass each time you board a bus or vaporetto. Otherwise you have to buy a ticket at the kiosk each time you want to board.