The Aberdeen-based company made £1.9 million pre-tax profit in the six months to December, compared with £1.73m in the first half of the preceding year after enjoying record demand for its wellhead technology.
The company claims the technology, which was developed by Mr van Bilderbeek, offers a more cost-effective way of ensuring that wells are properly sealed than alternatives.
AIM-listed Plexus won orders from big names such as Statoil and Centrica in the North Sea in the past year.
The company increased its presence in overseas markets by winning its first business in West Africa from Glencore in Cameroon.
Plexus's chairman Jeffrey Thrall said: "The group continued to make good progress in the first half of the year as we built on the record performance and activity levels reported at the last year end."
He said Plexus was confident of achieving growth during the current financial year and beyond.
Signalling confidence, the company increased the interim dividend by 9% to 0.48p per share - up from 0.44p last time.
The company believes it will benefit from a big increase in global exploration activity in areas featuring high pressure and high temperatures, as oil and gas companies widen their search for resources.
The company says its POS-GRIP system is well suited for use on wells in such areas.
Mr van Bilderbeek, who is Dutch, was pleased George Osborne included a tax break for firms operating in high-pressure and temperature areas in this month's Budget.
The company hopes this may help to encourage exploration activity in its core United Kindom continental shelf market following a worrying slump in drilling in 2013.
Mr van Bilderbeek added: "I was delighted to note in the Budget last week that the Chancellor further endorsed the Sir Ian Wood report published in February 2014 aimed at maximising recovery of the UK's remaining oil and gas reserves when he said that he would 'take forward all recommendations'."
Sir Ian, former head of Wood Group, recommended the Government urgently assess the potential to stimulate exploration.
Graham Stevens, finance director Plexus, noted firms can get generous tax breaks for exploration in Norwegian waters.
Asked if Plexus had any concerns about Scotland possibly voting for independence in the referendum in September, he said whoever was in power after the ballot must maintain fiscal and regulatory stability.
Mr Stevens said Plexus is "fiercely proud" of its Scottish roots. He noted the business competed successfully against international giants like GE and Aker.
Mr van Bilderbeek founded Plexus in 1986 after working for oil services companies including Vetco.
He won the Entrepreneur of the Year title in Grant Thornton's Quoted Company Awards for 2013.
Plexus employs 140 people in Aberdeen in areas like research and development. It out-sources manufacturing.
The company noted a share of its future profits will qualify for the 10% rate offered under the Patent Box scheme. This applies to profits attributable to UK and European patents.
Shares in Plexus Holdings closed up 4%, 12p, at 284p.