The success of your tender is unlikely to be based purely on your price.
It's obviously a commercial job, so you could even go in more expensive but still get the job if you produce a good Risk assessment and Method Statement.
Acknowledge that you are aware that you are not the cheapest around, but neither are you the most expensive.
Sell your business to them in other ways. Show them why should they choose you.
Don't slag off the competition but just highlight what makes you their obvious choice.
eg. your training, a record of reliability, your h&s awareness, other high profile customers in the area.
I went for a big Hotel that was gathering quotes and got the job. The guy said to me afterwards that I wasn't the cheapest nor the most expensive, but he liked the look of me because I have an honest face. :

See if you can meet in person with whoever wants the tender. Face to face contact will go a long way.
Unless the price they are paying is a very good price, to go in cheaper would be just cutting yourself short. At the very least go in the same and let the best man win.
Mark