The Ospreys picked the same starting line-up that produced an eight-try triumph in northern Italy last weekend.
But the first points fell to Biggar, who punished a scrum offence, but that was cancelled out as Garry Law replied two minutes later.
In the opening quarter Viadana had more than their fair share of possession as the Ospreys struggled to gel.
The hosts could have fallen behind, but Law missed a simple penalty after 20 minutes.
But the Ospreys soon resumed something approaching normal service as a good scrum was followed by an excellent Biggar pass for Bowe to go over.
The sin-binning of visiting captain Quintin Geldenhuys - his second in two games - for disrupting an Ospreys' drive helped the team score two more tries.
Number eight Filo Tiatia, who drove over from close range after 32 minutes and he was heavily involved five minutes later as a combined move ended with Parker scoring.
Law struck just before the break with a penalty goal but the Ospreys upped their effort immediately after the break, full-back Gareth Owen got in at the left corner for the bonus-point try.
Biggar converted superbly from the touchline only for the Ospreys to then see hooker Richard Hibbard sent to the sin-bin for ball-killing and Law put over his third and fourth penalties.
Adam and Ryan Jones joined the fray, the Wales skipper recovering from the back injury that ruled him out of the Wales-Australia game.
But the biggest cheer of the afternoon was reserved for Adam Jones' keenly-anticipated return.
If the match lacked any real bite, it produced a frantic finish.
There were three tries in four minutes, Bowe going over for his second.
Then Viadana's Welshman number eight Gavin Quinnell, who grabbed Viadana's only try in the opening leg, intercepted and sprinted over from 35 metres.
Scotland wing Nikki Walker completed the day's scoring for the hosts.
Ospreys boss Scott Johnson:
"We set our stall out for this month to be in control of our pool or our destiny and I think we're just about there now.
"We control how far we go in this competition. We're not relying on others so whilst we didn't play well today, we're happy with where we are.
"It wasn't a fluent game and we love fluent games. We've got to be critical of ourselves - there's aspects of our game we're really disappointed with.
"The reality is late January there's two beauties to play [against Clermont Auvergne and Leicester] and whilst everyone could argue that our pool's had a so-called easier team in an Italian team, I think we've countered that - the three teams left in our pool - each one of them in their own rights could win the European Cup.
"So I think we've got a pretty tough old pool to finish with."
Ospreys: Owen; Bowe, Parker, Bishop, Walker; Biggar, Januarie; James, Hibbard, Mitchell, A. Jones, J. Thomas, Collins, Holah, Tiatia. Replacements: Hook for Parker (58), Spratt for Bishop (72), Nutbrown for Januarie (72), Bennett for Hibbard (58), A. Jones for Mitchell (58), Evans for J. Thomas (66), R Jones for Tiatia (51). Not Used: Griffiths.
Viadana: Law; Pratichetti, Harvey, Cox, Sepe; Johansson, Wilson, Sciamanna, Santamaria, Elosu, Hohneck, Geldenhuys, Persico, Krause, Sole. Replacements: Pace for Harvey (29), Hola for Johansson (70), Ferraro for Santamaria (51), Milani for Elosu (39), Benatti for Persico (60), Quinnell for Krause (54). Not Used: Cagna, Brancoli.
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