Neser, who proposed to his fiancee Olivia last month in a light plane flight over South-East Queensland, claimed 5-32 from 17 impressive overs as he assumed the role of senior quick for the Bulls.
The Australian squad player ensured the Tigers were kept to 250 on a good Park 25 wicket in Adelaide as part of the COVID-19 Shied hub.
Neser, a member of the Test squad that retained the Ashes last year as well as the subsequent home campaigns against Pakistan and New Zealand, is yet to play a Test match and was unavailable for the recent limited-overs campaign in the UK after suffering a groin strain during the winter.
The 30-year-old made his comeback for Gold Coast in the Queensland Premier Cricket competition late last month, and duly stunned Tasmania on the first morning of their clash against the Bulls at Gladys Elphick Park in Adelaide where he claimed three wickets in the opening session.
The Bulls could have had the Tigers out for even fewer runs, reducing their opponents to 7-149 after a double strike from Xavier Bartlett removed former Queensland Ben McDermott (74) and Test captain Tim Paine (4).
But a wagging tail, built around 54 from Beau Webster and 33 from new recruit Peter Siddle, lifted Tasmania to 250.
Bartlett finished with 4-58 after some early treatment, while leg-spinner Mitch Swepson was solid throughout with 1-68 from 27 overs.
The Bulls got to stumps at 0-7 and will look to their top order to consolidate the chase today.