The Ravens boss also wants the likes of the Blues and Leyton Orient to regret giving up on the 28-year-old after he made a return to the Hayes Lane outfit this week.
Dennis has re-signed for his former club following a successful trial that included a stunning goal in a friendly against Fulham under-23s.
It ends a frustrating three-year spell in the Football League which began with a free transfer move to Pompey in July 2018.
Under then Blues manager Kenny Jackett, the attacker made just eight appearances during his one and only season at Fratton Park.
That consisted of just a single League One outing – a January 2019 cameo off the bench at Oxford United during which he claimed an assist in a spectacular Brett Pitman goal.
He was subsequently sold to Leyton Orient for a fee of around £40,000 in August 2019.
Unfortunately, Dennis failed to flourish at Brisbane Road also, despite 49 appearances and four goals during a two-year stay.
He was released at the end of last term – before Jackett took over at the O’s – as Orient finished 17th in League Two.
Now back at Bromley, where he scored 47 goals in 156 appearances between 2014-18, Dennis’ career has come full circle.
Woodman believes the player has ‘the bit between his teeth’ following three forgettable seasons.
And he’s determined to make the most of Dennis’ presence as both look to prove his doubters wrong.
Woodman told the club’s website: ‘I’m really chuffed to get Louis in the building.
‘He has the bit between his teeth which is great, and he has an affinity with the football club.
‘But that was yesterday, and we’re here with Louis Dennis today.
‘I think he has unfinished business not only here but in his career, where he’s been unfortunate really in the sense that he’s had a couple of good moves which haven’t worked out.
‘My job is to make sure that Louis Dennis makes everyone realise what a mistake they’ve made not bringing him to their football club.
‘I’m delighted to have him, he’s a great professional and character, and it’s exciting to have him in and around our club.’