Mr Foster-Bell was not available for interview. In a statement he said he believed his travel was within rules and for a Parliamentary purpose.
He would not provide details about what travel was funded last year.
Last night Newshub reported that Mr Foster-Bell had 12 staff leave in a period of three years, with one saying he was a "bully".
Other former staff said they left on good terms.
Mr Foster-Bell has two full-time positions funded for him, and it is unclear how many of the staff who left were employed part-time.
He would not clarify that or answer other questions about staff turnover or allegations of mismanagement, saying in a statement that "it would be inappropriate for me to discuss employment matters".
Mr Foster-Bell is 46th on his party's list and the negative press could worsen his prospects of holding or bettering that position.
He entered Parliament in May 2013 following the departure of Jackie Blue, and unsuccessfully contested the Wellington Central seat in 2011, Dunedin South in 2002 and Wellington Central again in 2014.
Mr Foster-Bell remained on the list after losing out in March 2014 to Shane Reti for National's nomination for the Whangarei electorate.